I split used 2" belts in half all the time. Works fine for me.
The primary concern is not the belt width, but the method used to track the belt. There are two methods used- center tracking and coplanar tracking.
Most equipment we run across will use the center tracking method, which means a crowned tracking wheel. A crowned wheel means that the belt will naturally ride towards the high point; a real plus is that now it makes no difference if the belt is 2" or a quarter of an inch, it will self-center with minimum adjustment on our part.
Coplanar tracking is generally reserved for the wider sanders prevalent in woodworking, and certain bandsaws.
In this method, the tracking wheel is completely flat, and the belt (or blade) is tracked properly by adjusting a wheel to be coplanar with the opposite wheel. This requires very fine measurements and adjustments to work properly and takes a lot of time for initial setup, so it is generally only reserved for equipment for which a crowned wheel is not suitable. Think very wide belts- I have used door sanders with 56" wide belts. Or a bandsaw designed to run blades in excess of 1" because a crowned wheel would induce too much stress on the blade, causing premature blade breakage.
Bottom line- if you already have a belt grinder, it probably (but not always) has a crowned wheel. Using narrower belts is simply a matter of splitting the wider belts. So now the bigger concern is belt length, and whether your machine will accommodate that length.