Politics shouldn’t be about owning the other side. The Dems should not vote outside their party unless they have a deal to do so.
However, yes, the Dems could help to vote in a moderate speaker. They should negotiate concessions to do so. Doing so freely would be bad politics. It would give the far right fodder to rile up their base. It gives the moderate Republicans no reason to fight back against the far right and gives the Dems no win a part from the Republicans enacting their policies, which often is against the Dems policies.
Purposely inflaming the far right only emboldens them. This is one time the high ground actually works to penalose the far right and make them less effective.