Let's say there are 20 skills and we have a 5 man party. If each PC is good at 2 skills from a supporting background that means they have half the field covered. If half of them also picked a race that give a skill that's ~2 more.
So if a 5 man party can pick up 8 skills between them with class/subclass/spells/summons/items options they can have the entire field. It's not even a reach to have some of the high impact ones to have 2-3 PC deep redundancy in place. Now expertise is dirt cheap could also plan for 4-5 to be covered that way as well.
But you are already going to have overlap in those initial skills.
So, your initial 10 or so class skills is more likely 7-8 skills due to overlap. Your 10 background skills are likely to see overlap, both with other backgrounds
and with skills from other PCs' classes, so I would estimate maybe another 6 skills are covered.
IME that brings it to a more realistic 13-14 out of 18 skills. That leaves 4-5 uncovered skills. You might pick up 1-2 more from race, but IME again most of those skills are likely already covered--so more overlap. Not a big deal, a lot of skills aren't as useful as others anyway. Also, a lot of those skills will not be in abilities with higher modifiers, so the total bonuses suffer.
Frankly, I wouldn't say Expertise is dirt cheap. It is either a feature or feat, both of which are limited for everyone, so the cost is there IMO.
The point of the skill monkey is to take up the burden of overlap and/or expertise. So, the really important skills have a +6 or 7 (or better) instead of a +4 or 5.
Finally, I am not saying having a skill monkey is essential in any group, just like a dedicated healer isn't essential, but they sure can help in a lot of situations either by supporting PCs with good selected skills or by taking the lead themselves.