Big parties in MMP and other proportional systems have ideologies and stick to their ideologies.

Not really because big parties get more seats. In a voting circle with less people there will only be 1 or 2 seats available for that circle, so, they will go either 2 for the gov party or 1 for the gov and 1 for the main opposition party.

Smaller parties will only elect seats in the capital or big cities, which means if you want to have a political career you choose the party that more or less aligns with you from the big ones.