My only concern with using the 10 gallon cooler for partial mash small beers is that you may end up with the grain bed too shallow to reasonably act as a filter.
I haven't seen anyone mention the coffee lid trick in response to this concern. Just throw a coffee can lid on top of the grain bed and pour any liquid you want to add to the mash on top of the lid. The lid will disperse the impact of the liquid.
If you batch sparge then bed depth won't matter and a 10-gallon cooler will work fine for smaller batches.
True, but you may still need to reintroduce liquid into the mash during vorlauf. I batch sparge, but I use the coffee lid for this vorlauf step.
As for tun size, considering my 48-quart cooler can be a bottleneck for really big beers, I recommend the 10-gallon at least.