Two points about housing.

1- standard brake housing is a fully compressed coil on coil spring. As such it's already pretty compressionless. Sometimes people mishandle it, and make overly sharp bends which cause the spring to relax (move from compressed coil on coil), which will make the system feel spongy.

2- so-called compressionless housing will often make a cable feel firmer, but is prone to two typed of sudden catastrophic failure, which make it unsuitable fro brake use.

a- because the wires are nearly lengthwise, the compression load when the brake is applied causes them to bow outward. This is resisted only by the plastic cover, which has limited strength and can fail, especially if degraded by UV and time. Some housings prevent this by wrapping Kevlar or CF around the wires under the plastic. These are rated for brake use.

b- regardless of whether the housing is buttressed, the lengthwise wires tend to work to the center where the end meets the typical conical bottom ferrule or brake fitting. This can cause some binding, and in extreme cases can extrude through the fitting leading to failure. The issue can be solved with flat bottomed ferrules of sufficient strength to handle the load.

So compressionless housing can be used, if it addresses the two limiting factors. But may not solve the real problem, which I suspect may be sloppy fits at the ends. Take the system apart, and grind or file the housing ends flat so they sit squarely in the fittings. Then do a few hard squeezes to settle everything before adjusting the brake.

Other issues may include non cable flex, such as the brake lever arm or parts within the brake.