The majority of my 5E play has been feat-less (and quite a bit with just Basic/SRD classes). I'm most experienced with low-mid-level play. We've done some play at 15th or so and a 20th level one-shot that ran 3 sessions so I am not fully versed on high-level play in 5e.
In my experience, everything can be balanced with an astute DM using encounter/adventure design and careful magic item drops without using house or variant rules. That being said:
1. Strength v. Dexterity. Dex is a better (i.e. easier to build and with more apparent applications) as a general rule. Adding challenges that require Strength goes a long way here. Put in things that need to be pushed, dragged, lifted, broke, bent, etc. Environmental effects (strong winds, rushing waters, falling rocks) that require Strength saves to avoid being knocked down and taking damage are also good too. I generally stay away from tracking encumbrance because due to utter boredom, but requiring a PC to have sufficient Strength to haul out a treasure chest or fallen ally is fair game. Giving out Strength-based magic weapons also helps.
2. Melee v. ranged. Ranged is better, but putting in lots of cover, having enemies use that cover, using waves that come from different directions, having enemies appear at point blank range, and otherwise keeping pressure on the whole of party fixes this while playing without feats. Giving out magic melee weapons more than ranged also helps.
3. Martials v. casters. Again, this sort of thing is over-stated and problems are often a matter of adventure/encounter design. Casters have limited slots per day and so it's subject to attrition, much like hp. Put in quick challenges designed to drain spell slots. Even a need to cast detect magic takes a 1st-level spell slot if they don't have time to cast it as a ritual. On the flip side, you don't want your caster players too comfortable using their slots lest they need them later. Always giving them something to worry about, even if it doesn't come to fruition (even a red dragon spotted flying in the distance might make them more cautious). Never reveal the extent of the challenges before them. Obscure as much as possible until they make the effort to scout, research or explore. And, obviously, building in lots of uses for mundane skills will also help.
In my opinion, the biggest balance issue in 5e is not any of the above, but short rest classes v. long rest classes. Generally, you really need to put long rest classes through the wringer to challenge them and have to purposely build in "picnic time" for the short rest classes or they burn out. Figuring out how to manage both of those consistently for your group can be a chore. However, as every group and DM has different expectations in how adventures should be build and played, there's no hard and fast rules.
