A shower that has gone stiff to turn, or will not settle on a temperature, is almost always the valve hidden behind the wall.
You may not need to lose your tile
This is where real money is saved. Many valve repairs can be done through the existing trim plate, or through a small opening in the wall of the room behind — often a closet. Before agreeing to a quote that involves removing tile, it is completely reasonable to ask whether the valve can be reached from behind. Very often it can.
Older tile is hard to match
Bathrooms here from the fifties and sixties often have tile that is simply not made any more. Working around it takes a little longer and is nearly always worth it.
Water going cold suddenly
If the shower turns cold when a tap runs elsewhere, the valve has worn. Beyond being irritating, it is how people get scalded, so it is worth attending to.
A stain on the ceiling below
Usually the shower base, the drain connection, or grout letting water past. Three different repairs, and working out which before opening anything is the difference between a small job and losing the bathroom.