2 days a month isn't a big deal at all. I'm in the UK, and regularly travel anything from 2 to 8 days a month to a role in Germany and the Netherlands.

Fair enough. Would be a hard sell to spend 1/4 of my time away from family though.

If I may ask do you pay for the travel or do you get reimbursed by your employer?

I can't imagine any scenario where a company is requiring monthly travel and not reimbursing for it.

And even assuming 1 full travel day on either side, 4 days a month is a LOT less than 1/4.

I think you missed the point, it's about distances, and logistics, not days. Flying from UK to NL/DE doesn't sound particularly impressive: relatively short, non-hostile checks, accessible airports, wide selection of flights. Actually, it's more or less equivalent to getting to Bilbao from Iberian peninsula area.

Why should they specify anything? That you are not willing, it's ok. However, I know of people from California doing this on a monthly basis (traveling over Europe). For some people it's ok.