Well, if you do your own maintenance and plan on keeping the truck for a long time, it wouldn't hurt to buy the tool and have it for when you do need to replace the belt. Also, the service manager might be able to put a different brand of belt on since you know them personally. I'd ask and see what they say.
I understand the frustration part in regards to waiting for it to get repaired as I've been in your shoes before with another vehicle. Was some of that due to an employee shortage or because they couldn't get the parts in? If so, I wouldn't put that on the truck.