historically the filibuster has been used more to kill bills coming from the democratic side.

thats because dems are expected to actually pass legislation. thats how we have made progress in a bunch of areas in this country. through dem legislation. which now gets blocked almost universally by republicans.

obamas presidency was obviously an example of this on steroids.

repubs are basically just expected to cut taxes/regulations and install judges. they can do most of that through the reconciliation process (requiring simple majority), congressional resolution act invalidation (simple majority), federal judiciary confirmation (simple majority), changing rules or level of enforcement at the agency/dept level (with appointments requiring simple majority).

the other side of the coin...repubs are more likely to have a senate majority (for reasons you stated). which is going to make it necessary for dems to filibuster a lot of their far right legislation.

its prolly not in either sides best interest to nuke the filibuster at this point. and they both recognize that.