Why h-parameters of BJT are no longer popular?
A good question, with answers that will be somewhat opinionated (but here goes, with that caveat)...


Those AC h-parameters are all greatly affected by bias conditions. Presenting those variations in a data sheet is a problem.
Notice that S-parameters are still used widely, especially for MMIC devices run with fixed bias conditions. Measurement apparatus allows S-parameters to be found easily. While H-parameters could be measured (or derived from S-parameters), what would be the point? Those MMIC devices will likely be used in a near-50-ohm system anyway.
Circuit analysis software like SPICE can do a better job than using matrix circuit analysis techniques that would also employ y-z-a-parameters. And SPICE can handle non-linearity too, while matrix analysis cannot.
Perhaps h-parameters were more important when single active devices were costly, and every bit of performance was required of every device. Now we design circuits with ICs having excess gain that is used with feedback to make near-ideal circuits. Somewhat brute-force, but widespread.