Parson's bonus is only 2 (TBFGK 40a), which is pretty low.
1. This applies to all units of his capital...
2. But there's an additional bonus to units in the same battlespace as him...
3. And another bonus to units in the same hex as him...
4. And yet another for units in the same stack.
(The exact number for battlespace, hex & stack are unclear at the moment, but guesses are in the range of +1/+1/+1, so maybe +4 to all units not stacked with him)
From First Intermission 33, we know Wanda's bonuses are
No, Parson's bonuses are crappy.
HOWEVER! He SAID that GK needed all the bonuses it could get, and that the new Chief Warlord should be someone who's there already. Maggie getting him appointed again severely weakened GK's position, and since he can't actually resign, drag Stanley back up, and get someone else appointed, it's up to Parson to haul ass over there and provide what little bonuses he can.
On top of that, he didn't expect Wanda to stick her head into the MK and get stuck there. He thought she was going to stay in Spacerock and keep boosting the troops.
The real reason that Parson has to go into battle, though, is that his conscience won't let him direct a battle he wouldn't participate in. Is this dumb? Yes. But it's not about strategy here, it's about what he can live with at the end of the turn. (Parson talks about it in LIAB 42, which was a while ago)
"Are you always so pessimistic?"
"Not at all. I saved it for my last battle."