The Speaker is a highly political job. They decide which bills will get a floor vote and which bills will not get a floor vote. One of their first decisions will be whether to bring a budget bill with Ukraine funding to the floor, or a budget bill without Ukraine funding. They will need to decide one or the other before anyone votes for them as Speaker.

If an "apolitical" outsider plans to include Ukraine funding, they would put many Republicans in a tough spot. So why exactly should they have support from those Republicans? If they plan not to fund Ukraine, why exactly should they have Democratic support?

Likewise, will the "apolitical" Speaker bring pro-choice bills or anti-choice bills to the floor? Pro-LGBTQ or anti-LGBTQ? Pro-union or anti-union? Pro-environment or anti-environment? And so on. Whichever they choose, it will cost them support.

Legislators favor certain bills, and they won't vote for a Speaker who won't bring those bills to the floor. Even if they have a Medal of Honor.

Several decorated war heroes have gone into politics, including GHWB, McCain, and Inouye (who actually had a MoH himself). They didn't automatically get bipartisan support based on their military record. If 212 Democrats somehow nominated and voted for someone with a Medal of Honor, that person would immediately be labeled a Democratic war hero, like Inouye. And they would get as many Republican votes for Speaker as Inouye would have: zero.