As blind vias cost more money, so can you avoid using the blind via? And board layer counts are always even numbers as a result of the manufacturing process.

A common way to avoid what you do not want is to run copper to where they can be tolerated.

Why do you need to make a blind via instead of a thru hole? Have your board design used no -thru-hole rule?

You can ask your PCB manufacturer to send the quotation of 4 layers PCB with blind vias.

Very interesting post.