As a side note the reason the bearings have a loose feeling when cold is just that. As they heat up the clearances tighten up. It is the noise, roughness, and extra sloppiest that you got to worry about.
Sometimes it is not even the bearings. I just repaired a JD Z425 deck last week where it was the spacer bushing that was the problem. Someone in the past installed a new idler pulley and assembly it wrong which lead to the bushing hour glassed. So instead a $60 pulley is was $5 bushing.
BTW these companies have gone bonkers on the prices for these parts. I pickup a 3/16 x 1 x 48 piece of metal yesterday and it was $13. But had to have it for a deck project so the customer getting the bill. At least the local price is better than ordering it. No wonder I save every piece of flat and angle iron I come across.