Your friend is wrong. It's an imperfect proxy, but looking at programs that do work, speed is a good proxy for quality, because speed means someone gives a damn. There are good programs that are slow, but bad programs all tend to be bloated.
Of course "speed" is something to be evaluated in context. In a group of e.g. 3D editors, a more responsive UI suggests a better editor. A more responsive UI in general suggests a better program in general.
> this (speed) is never a measure of a program's quality. Is this universally accepted?
Universally? No. It all depends on who you ask. Companies tend to say speed isn't, but the truth is, a lot of companies today don't care about quality at all - it's not what sells software. If you ask users, you'll get mixed answers, depending on whether the software they use often is slow enough to anger them regularly.
Especially when you’re doing the same task “template” on a day to day basis, even 1 second per input adds up quickly.
In many cases I'm happy with simple but slow but fast enough.