Being stronger is always better; the problems are when (due to diminishing returns) you have to spend more and more hours training for less improvements. For example, a regular guy could probably get to a 300lb bench, 400lb squat and 500lb deadlift in 2-3 years of lifting 3 hours a week, but for a guy to get to a 400lb bench, 500lb squat and 600lb deadlift you are looking at 4-5 hours lifting per week, and the progresion slows even more despite training longer and longer as you try to improve.

Another problem we have is the confusion people have when discussing strength - the term is terribly missused and means all kinds of things depending on who's talking and what they are talking about. The easiest way to define strength is the ability to exert against an external resistance, ie. lift heavy stuff. Not lift it fast, or over and over again and again, or lift your bodyweight, or throw/puch/sweet roundhouse moves, just move the heaviest thing you absolutely can, and that is what powerlifters do; this is maixmal strength when we are getting really specific, but in general conversation is the 'default' meaning of strength.

Of course, lifting at your limit, if you can produce x amount of muscular force and are lifting x-1 mass, it will be a very slow lift. This will strenghten muscles, bones, tendons, ligaments and help with generally being harder to hurt/injure, but will not make you fast, flexible, increase your endurance (although it will somewhat as it will make everything you do outside of lifting easier as it requires less% of your maximal strength to do), or increase your cardiorespiratory fitness much. It does heavily influence all the otehr types of strength (and many other aspects of fitness to boot), and as such is an important one to improve.

Another type of misnamed strength would be power - the ability to exert force quickly - like throwing, punching, jumping etc. where you have to be as strong as possible, but only have a split-second to create all this force before the external resistance is no longer there to be exerted against (can you jump slowly? No, you have to create as much force as possible before your feet leave the floor). This explosive strength is very useful in a combat situation, as you can litterally move quicker about your opponent and hit them harder, faster. It will lead to some improvements in your anatomy, but not as much as the strength training would, because you are subjecting it to less resistance (because you can't move soemthing fast if it's really heavy), so your body will not adapt to resist such extreme forces, because it is not required to (although the forces created in power movements can get really large, they are not at that level for very long during the lift, nor for very much of the range of movement so the full kinetic chain involved will not get the training effect as such). This goes really well with maixmal strength training as the two compliment each other, ie. by training one you will improve the other somewhat, and they have a kind of synergic effect upon each other.

A third type of misnamed strength is strength-endurance, or the ability to continually exert a submaximal force against a constant resistance. This is often encountered in actions like arm wrestling, tug-of-war, some aspects of wrestling and grappling (such as chokeholds and applying/resisting locks etc.), and also submaximal power strength (such as being able to punch effectively for twelve three minute rounds; the person who can punch well later will be at a significa advantage against the guy who tires midway throug the bout). This is a specific type of adaptation to lifting multiple repetitions, and is as much about neuromuscular efficiency and anaerobic metabolism (training the muscle fibres to fire in coordinated groups so some rest while others work and vce versa, and the ability of your body to continually supply the working tissues with all their energy needs and remove the metabolic waste from the area), and is part of what is meant when you refer to the ability to continue fighting effectively for sustained periods.

Bodyweight strength, or strength vs. size is another distinction, and although it isn't actually a type of strength per se (it is still the ability to exert force against resistance, it is just in this case the resistance is fixed as your bodyweight), it is a measure of how much stronger you are compared to your weight, affecting how powerful you are lifting yourself and how long you can do it for, or else how strong you are relative to your size. Because force production relies primarily upon muscle size, and muscle contractile force is perfomed by the muscle fibres, the cross-section (or two-dimensional area) of a muscle is a fair indicator of it's force production potential - however, the muscle itself will grow in three dimensions, so you will get stronger squared vs. getting heavier cubed, which is why, relatively, smaller lifters are stronger than larger ones, despite subjectively the reverse being true. It also gives a clue as to why (apart from training methology, resources, diet, goals, time constraints and specialisation) soldiers and the like are not all hulking behemoths - they tend to have a set weight to carry/move, but mostly for extended durations, so they adapt to lifting that load. Also, they are kind of self-selcted against the giants because of these parameters (overall, a 350lb strongman would make a poor soldier because of the above problems, although they can make for an exellent fighter, the demands are two completely different kettle of fish).

I have typed this all from the top of my head, so it no doubt is not as accurate as would be ideal, but it gives you all some idea of the topic. There are many other factors involved, an example being flexibilty and why powerlifters, bodybuilders and the like get stuck with being the default 'muscle bound creaky-old wrecks' end of the spectrum:

They train specifically for their sports, and only aim to be as flexible as required to succeed, generally. Anything past that would be a waste of their time and could even impair their performance (for example, a powerlifter will often be as flexible in the hamstrings as they need to be s othey can squat to parallel - if they further trained their hamstring flexibilty, they would not get as much of a 'bounce' - or stretch reflex - from their hamstrings at the bottom position of the parallel squat, which would reduce their poundage. You could argue that they should be squatting below parallel, but it is uneccesary further range of motion during a competitive lift that they needn't perform, and one of the distinctions of lifting for health & fitness vs. lifting for sport). Additionally, they often get compared to gymnasts and the like, who dedicate many more training hours to flexiblity, as it translates to better athelitic performance for them. A strong man could quite easily become very flexible if they chose to dedicate the time and adaptative ability towards it (indeed many do, an example that springs to mind would be Mirco Cro-cop's high kicks, or Jean Claude Van Damme), so strength doesn't equate to inflexibility as much as most laymen imagine it would - although there is some restriction around a joint where the added tissue mass impedes upon itself, it doesn't make much defference because a) muscles and tendons are squishy, b) most of the mass increase is at the muscle belly, not the joints, and c) who really needs to be at the extremes of human flexibility, when they would be better off spending their time improving another aspect of fitness or sport/combat secific training - similar to the extremes of maximal strength, it gets to a point where the benefits do not justify the time~effort costs.

Again, as it is all written as i pull it out of my backside, the language and terminology is probably not as precise as the topic requires, so if any parts do not read cleary i am happy to clarify anything, which being it's own neat little summary will probably be easier to both write and read!