At London Heathrow, the tower controller will tell you to contact ground and give you the frequency while still on the runway (on roll-out when you hit about 50kts). The pilot monitoring will then change frequency and say “ground [callsign][runway exit number]” and the ground controller will respond “[callsign] good morning” and then straight away give an initial taxi instruction like “2nd right Bravo, left Foxtrot, hold at Foxtrot 1” or “turn right on Bravo, hold short of Lima, stand 248” and there’s usually a follow up instruction when/if they reach a holding point to take them onto the stand.
This ensures continous flow at busy airports, without having planes stop after exiting the runway while they wait for their instructions, blocking taxiways.
It would be nice if BATC could be a bit more pro-active like this and not require aircraft to be completely clear of the runway before the handover. It might also be a good idea to allow for taxi instructions to be split up into smaller chunks like LHR do, to minimise the amount of overwhelm for the pilot.