Most challenging and wanted DPS class?

[Idolon]

However, unless 4.05 really rectified a lot of MCH's Stormblood redesign, they are still not dealing as much damage as an equally-skilled Bard. Again, that's if 4.05 didn't fix the glaring issues with the job.

4.05 buffed MCH damage slightly, but made the glaring issues with the job even worse. According to data on FF Logs, MCH and BRD are fairly evenly matched up to the 75th percentile, but the most skilled BRDs are able to do significantly more damage than the most skilled MCHs.

Then we have MCH, with a moderately high skill floor and a very high skill ceiling, but right now it's in a pretty bad spot since it's outclassed by brd in every possible way and scenario while also being harder to play at a high level. But if you're looking for a challenging job, MCH is a good pick and it's very fun to play.

If OP is looking for a challenging job, it's not MCH. It used to have a moderately high skill floor in 4.0, but after 4.05 it has a fairly low skill floor and equally low skill ceiling. Avoiding overheating now requires little effort beyond remembering to use Cooldown once every 30-60 seconds, and in the event you do accidentally overheat, it takes so long to have done so that Barrel Stabilizer is almost certainly available to use again, making overheating not much of a penalty. The only things that are particularly challenging now are the things that shouldn't be challenging, like recognizing that overheat + Wildfire is rarely good even though all the tooltips lead you to believe they're intended to be used together, or actually forcing an overheat for the rare situations where it is useful.