Is \$f_{\text{hfe}}\$ independent of BJT capacitances?
As you probably know, \$\beta\$ or \$H_{\text{fe}}\$ is in first order determined by the ratio of the doping of base and emitter. This doping ratio is intrinsic (determined during manufacturing), it has no frequency dependency. What does limit the frequency behaviour though is the carrier mobility. This explains why there are Silicon-Germanium (SiGe) based Bipolar Junction Transistors which have a higher \$f_{\text{hfe}}\$. The SiGe has higher mobility resulting in faster transistors. SiGe is not the only option, for more look here.

You are correct in that all (parasitic) capacitances also limit the high frequency gain of BJTs. However, in high frequency designs it is common practice to make these capacitors part of LC resonator tanks allowing them to be tuned out. Meaning they form a resonant tank with an inductor and thus eliminating their frequency limiting effect.

I think it depends on how far away a design is from the \$f_{\text{hfe}}\$ limit to decide if you can ignore \$f_{\text{hfe}}\$ or that you have to take it into account. If the \$R_{\text{input}}\$ and \$C_{\text{bc}}\$ are limiting, then you can neglect \$f_{\text{hfe}}\$. That's what experienced designers do to make their life easier ;-)