The "one or more nonland" restriction is to avoid two sources of grief: you can tap all of your lands to make your opponent have no mana on their turn, except you can break the symmetry by ramping or by having instants; and when you attack with several creatures, you can still only tap one of the defender's creatures, rather than getting a free alpha strike

Now I understand why Wizards sometimes makes cards that could be cool but suck instead

Tapping is weird with "one or more", e. g. tapping creatures to cast a spell with convoke would be grouped as one "one or more", but if one of them is an Elvish Mystic, I am able to tap them beforehand and float the mana for an additional trigger?

Yeah. That's another reason I excluded lands, since you can float mana one at a time before casting a spell