As always your contract is with the shop, *they* may have to wait for the replacement from the manufacturer/distributor but what they do in the mean time is entirely down to them, it normally is one of these:
A > wait, and wait some more, making you wait as well
B > offer you a demo/shop bike to use until replacement arrives
C > use shop stock to replace your broken part on the spot*
Most shops go for option A as it’s the least effort for them and least risk financially on their part.
Decent shops will often go for B, especially if they know warranty turnaround is slow.
Really really good ones will do C, but since that relies on them either taking a financial hit or having a LOT of faith/good relationship with the distributor/manuf.
You can cut them some slack around new model years, availability or speed of replacements, but ultimately it’s down to the shop how far they go to keep you happy.
FWIW, 10 days is not unusual, but unreasonable? that’s more a matter of expectation and opinion.
* assuming they have stock, or can order stock, and that it’s nothing so niche that that’s not an option.