My entire first two paragraphs are directly related to your quote, which is why I quoted you. I want to know what builds your players are becuase you are making claims they got to level 15 just fine and therefore arguing that healing is not needed in 5e because of it.
First clarify, making to 15th level and "just fine" are not the same thing

Here are there builds. If you need something more specific let me know (PS we use all feats, no +2 ASI):
Variant Human Fighter Battlemaster
Variant Human Fighter Battlemaster
Variant Human Rogue Thief
Variant Human Rogue Scout (aka Ranger)
High Elf Wizard - Enchantment
I happen to largely agree with you, but I point out that one anecdotal story does not empirically prove that 5e as a system does not require healing or that healing is unnecessary. It is one data point at best. Other variables that might influence the evaluation of your particular group that I'd be curious to know:
1) How often does your group short rest or long rest? Do you often discourage them from resting?
it varies a lot, but we average about 3 encounters per long rest
2) Do you use any varient healing rules?
Yes, HP heals normally, but we have a 2nd pool of BHP (bloodied hit points). These are actual meat points and heal very slowly: 1/week of rest. When BHP = 0, you die (we don't use death saves), and these don't increase with level. The max BHP for a human is 10, but most of the group has less than that (since it is difficult to max stats).
3) How many healing consumables does your group use in a typical adventuring day?
Almost none. Healing potions are not a commodity in my setting. They are rare and expensive.
4) How many encounters (and what difficulty) do they typically have in any given day?
varies, but 3 encounters is the average. difficulty varies too, but I have never really tracked it. My players are old school and try to solve encounters creatively vs. jumping into combat at the drop of a hat. If they see an encounter that is to tough, they will retreat.
5) Has your party ever had to grapple with issues that do NOT revolve around killing x number of y mobs and if so how did they accomplish it and with how much difficulty?
All the time, it just depends on the scenario. It is not completely uncommon to have encounters they can't handle simply with brute force.
Again I agree with you that I don't think the game requires a healer to function, but a single data point is a poor argument.
I was just trying to give a data point, not argue. I am fine with my group playing the game the way we play and enjoy it.