The threshold for me (and most people I think) is about 110ms between key strike and something appearing on the screen before something feels non-local and disembodied... which is good because I found I could get down to ~40ms local response time on a decent windows box. My 2015 macbook is about ~120ms for the terminal app.
That leaves 70ms latency budget to play with which can accommodate the the RDP overhead (~50ms) and the network hop (~10ms for me).
This whole journey started with me wondering if I should pay a small fortune for a better network connection, before I realised that most of the latency was in my keyboard and monitor!
I even built a Arduino Leonardo gadget to measure the lag systematically and some pcap software to spot the RDP packets on the wire. The code's pretty shoddy but it does the trick! You can see it and an example result with RDP here:
https://github.com/willmuldrew/lagmeter
Another big factor in the experience is jitter - so it's a good idea to ensure everything is plugged in if you can. Mice, keyboards and ethernet.
In essence, even if you have to RDP/remote into work, potentially you can still make it feel pretty local - don't give up hope!
At least until we arrange for everyone to have company provided dedicated work laptops which we can (mostly) lock down to the satisfaction of our clients and their auditors, but the switch to mostly remote working this year happened at roughly the same time as budgets were squeezed a bit (bet you can guess why!) so that hasn't happened across the board yet.
Allowing RDP from non-secured devices "for the time being" is iffy, but we are getting away with it due to the circumstances.
Latency is not really an issue to be honest. I think ping is about 15ms which is much less than the lag in this article. Right now I'm using the horrible, 2012-era work laptop with just Chrome running and there are delays typing this comment into HN which is a super lean site as it is.
The main downsides are actually
* crap single-threaded performance (don't think Azure has VMs over 3ghz except maybe the highly expensive GPU ones)
* Slow IO
* Video and audio over RDP really doesn't work.. no hardware graphics accel either... reduced ability to work on multimedia, we had one webapp where WebGL wound up behaving differently which we didnt