The core of make is really just a control flow model that understands file dependencies as a first class thing, and permits arbitrary user supplied actions to be specified to update those files. All those default rules around how to handle C files are really more like a standard library and can be easily overridden as desired.
IMHO what makes it annoying for projects other than C or C++ is that there isn't an equivalent portion of makes "standard library" that applies to e.g. java, but this is largely because java went down a different path to develop its build ecosystem.
In an alternate reality java tooling might have been designed to work well with make, and then make would have a substantial builtin knowledge base around how to work with java artifacts as well as having a really nice UX for automating custom workflows, but instead java went down the road of creating monolithic build tooling and for a long time java build tooling really sucked at being extensible for custom workflows.