You don't get feats at level 1 unless you are a variant human or custom lineage.
Getting your class's primary abilty score to 18-20 is often better than an feat. And you must wait until level 4 to take one.
For out of combatchecks, the ability score is often a teritary ability score for the fighter. Since most DMs do not use complex ability checks nor skill challenges, it is unlikely that the fighter has the highest value in a check or contest in a moderate to large sized party.
Custom lineage with a half feat is the only way to get an 18 at level 1.
If getting an 18 is of upmost importance as you imply then you should never play a race other than custom lineage. If you can't take a feat at level 4 then you certainly should not settle for a 16 at level 1. So by this logic you should always take custom lineage as your race right?
The only skill that uses strength is athletics and it is not used that much out of combat. That is why for out of combat use it is generally better to take a feat or to be honest even an ASI in another stat. You can boost charisma, intelligence or wisdom and get bonuses to a bunch of skills or take a feat that gives you skills or out of combat spells.
A fighter who takes skill expert in a skill he has a decent score in will likely have the highest skill in that party and some skills like stealth, perception and to a lessor extent investigation are used by all party members, so having the highest score is not as important as having a good score.
Finally the premise is simply not true, most parties in 5E do not have the 4E balanced design because classes are much more flexible and every character has to pull their weight. In a party for example with a bladesinger, hexblade and paladin, all combat optimized, the party as a whole will probably be better served if the fighter takes things not related to martial prowess. The party is plenty good in melee combat already and if he takes prodigy, skilled and skill expert at 4/6/8 that will give him thieves tools, 5 skills including 2 with expertise, a language and a +1 ability. At that point he has 3 more proficiencies than an equivalent level Rogue and expertise in two of them.
Let's talk about spells - a full caster gets 12 spells per day at 8th level. If you play a human or custom lineage eldritch knight and pick the right feats, at 8th level you can have a build that is a single class fighter, can cast 12 spells a day and has MORE cantrips than a full caster. At higher levels you are going to fall behind and all yours at 8th level are 1st and 2nd level, but you can cast just as many times in a day.