I'll add on that Aerospike engines tend to be popular with non-Aerospace engineers because they look cool. In reality Aerospike engines are optimizing for a design parameter space that doesn't need optimization. To draw an analogy to coding, it's like optimizing code in the non-crtical path. It doesn't really help you.
Rocket engine bells expand high pressure subsonic choked flow into supersonic low pressure flow. They are designed to do that most optimally for a given external pressure (if you try to expand the gas to a lower pressure than the atmospheric pressure then vibrations begin and can tear an engine apart because of flow backwards into the engine bell). Aerospike engines, if designed correctly, work by automatically optimizing to always expand the gas to whatever the atmospheric pressure is, maximizing total specific impulse over the flight. However they tend to have problems with cooling and so tend to be extremely heavy compared to other engine designs and you can equivalently design for this space by instead using multiple rocket stages, which all rockets do. More so, if you're trying to re-use rockets as is the current trend, having a heavy engine makes even less sense as you need to land that heavier engine.
Aerospike engine research made sense when it was the current fad to design single-stage-to-orbit rocket designs because they thought that re-using multiple stage vehicles wasn't possible. However that's no longer the case. Aerospike engines are a technological dead end.
Disclaimer: I am not an aerospace engineer, though I did take a couple of aerospace engineering courses before switching my major (turns out I wasn't great at the type of math needed) and I have a strong interest in the field and have talked to people in the field (and former classmates/labmates who are aerospace engineers).