Been running 5e D&D both online & tabletop for just over three years now. A few thoughts.
The monster creation rules are garbage, I just have to do it 3e style and eyeball a CR.
The encounter-building rules are also garbage, I do it 1e style and ignore them, which works great in 5e.
The rapid advancement from 1st to 3rd is one of those 5e things that works much better in practice than on paper, and has significant potential gameplay benefits when combined with 'bounded accuracy'. Unlike 3e-4e or even really 1e-2e, I can start new players & new PCs of current players out at 1st level alongside 5th level veteran characters. They can contribute to the group, and if they survive they can catch up fast, hitting 3rd in a couple sessions. And there is something very special about starting D&D at 1st level. Partly the new PC is easy understand, partly there is kind of a freshness to them, their whole life ahead of them, combined with a feeling of vulnerability.
XP - Been playing around with this a lot. The 5e XP system is over-focused on monsters I think, and tends to make wandering monsters a source of welcome XP rather than a threat. I was giving 1/5 monster XP but been finding that too little, and tending to over-award "quest" XP to compensate. Currently going with 0.5 standard monster XP, plus XP for gold looted from the dungeon & returned home. Did that last session & seemed to work; the party didn't do great on finding treasure so total was about 3/4 what they'd have got from standard full monster XP. 11th+ PCs will get only 1/10 treasure XP though, since 11-20 treasure awards are much bigger while XP per level almost flatlines.
Advancement Rate:
Overall for my sandbox Wilderlands I generally want an advancement rate of around 3-5 sessions/level, from 1-3 sessions at 1st-4th going to maybe 5-8 sessions at levels 5-10 and much slower, around 10 sessions/level, at 11-20. This is generally what I'm seeing in play with the XP chart as written, though with occasional spikes - 2nd level PCs carry off the orc hoard, or high level PC solos the dragon/lich/BBEG. That's great, advancement spikes are a good thing in my book.