Although tempted (like others) to get clearance while taxing I avoid this as much as possible. Clearance is usually available early enough to get it immediately after startup and I usually get it when warming up the engine(s). The exception (and it comes from time to time) is when ATC changes the clearance while you’re taxing (changing runway, changing SID etc.). And sometimes it means some benefit (like earlier takeoff) if you’re ready to accept the change of the game immediately. If they announce it and if it’s beneficial, I copy it, if not I postpone copying 
Regarding other stuff (like entering flight plan, learning SID, doing checks etc.) I try to discipline myself and avoid it, sometimes succesfully, sometimes not.
LeSving wrote:
You can request clearance at any time. I thought this changed everywhere a couple of years ago. In the last years we first request clearance, then request taxi. The ATC usually also repeat the clearance before take off, but then it is already memorized or written down.
I’m not sure why the original poster doesn’t do that. First request clearance, then request taxi. It’s what I have been doing as well. No sweat. The engine needs to warm up anyway.
As for doing “things” whilst taxiing. I don’t see an issue with that as long as you manage the risks. Taxiing is a low-workload situation, unless at a busy controlled aerodrome with confusing taxiways. In a low workload situation I see no issue with doing other things, as long as the risks are managed. Risks would be diverging off taxiway centreline, lookout, managing the engine and that’s about it.
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