In general I'd have less to focus on in combat. Having an abundance of refresh abilities doesn't make it impossible to fail at upkeeping. The refreshers just keep you from being punished by encounter design (gaps in combat). As a side effect they make poor buff management less punishing, but you're still going to be punished for using your out of combat refresher in combat by dealing no damage. I guess than leans the punishment away from casual play and more towards hardcore, but I guess that's OK.
For the ones you specifically mentioned, Enochian is fine and all of the above applies to it. I'm not as familiar with the other two because I don't raid with MNK or DRG but I know they tend to have more margin/refresh more often than Eno. That could be changed by reducing their time if it's a problem, or adding a risky alternative to refreshing them. They don't need to be removed or have their refreshes removed.
I see what you're getting at but in practical terms the buttons don't really cost us anything (and GL doesn't have a button if I remember). A one use button can be placed in the most remote spot on your hotbars without being a bother because you only need to press it once. Also while I tend to favor complexity over simplicity, adding more buttons is not the best way to make a job interesting. Having decisions to make and limitations to work with tends to create a better rotation in my opinion, and you can do that with a relatively small set of skills. I think BLM is a good example. In SB it was a little too Fire IV heavy, but Despair alone fixed that and made it a bit more interesting to play. I don't think the job needs any more skills at this point. If it did, there are some underused skills to revamp already (Scathe, Fire II, Blizzard I).There is no challenge in keeping greased lighting, you do it in the beginning of the fight and never worry about it again. Same with Blood of the Dragon. Imagine if those buttons didn't exist, you just started the fight with whatever buff they would give you. Now the buttons that activate and maintain them (few for dragoon, many for monk) could be replaced with abilities that are actually engaging to use.