Is targeting "closest" or "last" ever useful?

Yes there are situations where its useful.

For target closest, its useful for slow moving shots that can miss if the target is too far away, such as for the bomb tower. I usually set my bomb towers to target closest.

As for target last, its useful if you have aimed your tower down a long narrow path and you want it to keep shooting down that path instead of turning and following the lead balloon as it goes into a series of turns and wasting most of the shots. This is extra useful for a super monkey when placed at the end of a long straight way.

Both can be used for their own situations, in many ways (be creative and try to find new ways to use these "unused" targeting patterns).

This is an example of how I use closest. I place an Ice Tower and Missile Towers around it. The closest balloons are the ones that are frozen. Because the Missile Tower can pop frozen balloons, I set it to closest. It is then able to damage the frozen ones without targeting the non-frozen ones (and making it so the Ice Towers are only stalling the balloons).

An example of how I use last is with the Mortar Tower and its maxed out Specialty Building. I get multiple of them, and all set them to different targets. They will now most of the time target different targets. With that, the Stun effect and the Napalm effect are given to a maximum spread of Balloons.

As well as that, as said in the other answer, last can be used to make a tower attack down a long path. It works very well with the Juggernaut Catapult to fire a giant spike ball down the path.

In the end, those are all personal play styles, and there is no "best" targeting (besides first). But, if you do diversify your attack targeting, it can help you towers to not waste shots by going for different targets. Why have four Sun Gods attacking one MOAB when you can have each of them attacking their own targets and not potentially wasting damage?

Use for close: If you have a Bomb tower, it is a good idea to set it to close, because it will miss less. Use for last: Make a tower shoot along a path(like a 4/x Dart Monkey)