I'm not sure if unlimited short rests are a good idea. As someone who loves playing warlocks and multiclassing in DnD, I can assure you there are crazy shenanigans you can do if there is no limit on the amount of short rests you can take between long rests.
In my opinion the best way to discourage long rests would be to make it so that some things in the world happen based on the amount of long rests you took while still only allowing a fixed amout of short rests per long rest. In my opinion that would even increase the immersion. RIght now everyone tells me to hurry, but if I spend 10 days in a row only sleeping and eating, nothing really happens.
You could also adjust the game difficulty that way. On higher difficulties you'd have to do more encounters per day if you want to complete them all.
