Can you give an example why the active player wants to have priority in Beginning of Combat first?
I think the two different pieces here are in some sense independent. The opponent's floating mana makes you want to act in the beginning of combat step instead of the main phase, and holding a split second spell makes you want to act first in the beginning of combat step instead of waiting for your opponent to act.

Holding up mana here isn't necessarily about responding to the split second spell; it's more generally about having more options for actions to take, perhaps after the spell resolves. If you force the mana to empty from their mana pool, you cut off those options.

So, here is a scenario in which it matters that you specifically act first during the beginning of combat step: The active player has some mana available and Extirpate in hand, and two attackers with at least two toughness each. The non-active player has one floating red mana, two islands, Electrolyze in hand, and Feeling of Dread in their graveyard. The non-active player is better off casting Feeling of Dread, but they don't want to cast it during their main phase because then the active player could follow up with another creature, possibly with haste.

If the active player plays Extirpate during their main phase, the non-active player can use their floating mana to cast Electrolyze. If the active player waits until the non-active player acts in the beginning of combat step, the Feeling of Dread is no longer in the graveyard for the Extirpate to target. They get the best result if they act first in the beginning of combat step.