I'm sure specific services are hit or miss - there really shouldn't be a problem sending SMS to whatever number a user enters, but paternalistic snake oil salesmen gonna be paternalistic.
I've had the least difficulty with Google Voice (I believe it's impossible to tell "Google Voice" usage from bona fide Fi usage where it's really the users' only phone number). Voip.ms has worked very little for me, to the point of that I don't even try it. Heck I even used a voip.ms number for some online classifieds, and another person using Comcast/Xfinity mobile couldn't text me. I'm not saying this as a slight against Voip.ms itself, from what I've gathered most voip providers will be treated similarly.
One of these days when I get around to it I plan on setting up a wireless modem on a $3/mo paygo plan for my SMS nag needs. With a script that automatically brings the number as close to my paste buffer as possible.
What single use SMS service do you use? I haven't really investigated those.
These are definitely distinguishable, and some auth service treat them differently. Google Voice numbers come from a different carrier (the one named Bandwidth) than most Fi numbers.
This is called a "2FA Mule":
https://kozubik.com/items/2famule/
"A 2FA Mule is a mobile phone configured to forward SMS 2FA codes via email."
I turn it on when needed, which is almost never. When not job searching, the voicemail plays the classic "this line has been disconnected" tones and message on repeat for two minutes. WiFi calling means I can use it anywhere I have WiFi.
I get incredibly few spam calls using this strategy.