In no particular order... proficiency required - for the dex based skills acrobatics, stealth, sleight of hand, some performance - proficiency is not normally required. For some tools, it may be, but if those fit the character you can get that tool thru background. Thieves tool come to mind and tgry are easy to get especially with the create- your- own background default. So, there might be some I missed or GM specific but it's not the norm for DeX at least.I mean, if only one person get to roll then yes, the second best is useless and mostly just resorts to say "I help".
But the rest? It's always a good idea to ask everybody to roll just because the dice are fickle and you never know. So that is an interesting build... though, don't you need proficiency to attempts certain skill functions?
That said, I don't find the 5e skill system to be THAT engaging in itself...
Asking everybody to roll, in 5e, depends on the gsme. Default rules allow any ability check that doesnt meet DC to provide some progress eith setback if the GM wants. So, in a game where the GM doesnt just tun it binary pass-fail, then a lot of low bonus or no bonus rolls likely give you more trouble than its worth. The progress with setback is one of the more engaging aspects of the 5e skills for us.
But, in our games, it's not rare at all for the second best or others yo need to engage at things. So, having +5 or more in all the wisdom and dex skills gives you a lot of strong options to work with. It opens a lot of doors.
And all this still left the wood elf room for elven accuracy and sharpshooter at 4th and 6th, so by 7th had an 18 dex. Might have gone to 20 dex at 8th, dont recall. Course I saw a similar Samurai build that took one dex and benefits from the wisdom persuasion thing plus the samurai three advantsfecturns on demand to get sttong use out of sharpshooter with triple accuracy and useful non-combat skills in the dex and wisdom areas.