I train controllers not to use the word next, exactly for the reasons above. 'Vacate first (adding the word 'available' if the a/c is still going pretty fast) left/right' is spot on.
One more thing, is it correct to think that native English speakers sometimes don't realise that what's clear to them can be confusing for non native speakers?
Correct. In fact that is one of the hardest aspects of the job to teach/learn.
Taxi instructions that do not include letter designators should be banned
We can all agree on "C - D2 - K" - but may not agree on "straight ahead, then take the 2nd left...". So why not stick with the unambigous way of passing the instructions?
Because at some large airports, the configuration of taxiways, sometimes combined with poor signage mean that a/c sometimes get confused.
Phraseology such as
"Vacate right onto taxiway delta"
only works if it's said when the a/c is a way out on final. If I say that to an a/c on the rollout, he will either say 'which one's that, then?' or just aim for the one he was going for anyway.