I just realised that for a BJT at least at the fixed Ic the transconductance gm doesn't depend on a structure size. It's defined purely by the Ic itself
Indeed. It only depends on current. The power BJT can have higher transconductance if it passes a higher current, which it can do without burning. For example MJL3281 above a few amps of current... the few tens of milliohms resistance in PCB traces, bondwires, internal resistance in the chip, etc, set the limit on transconductance.
To elaborate on your question, a transistor can have a high current rating without necessarily having a large chip.
Big chip benefits:
More thermal mass -> larger safe operating area.
More contact area with leadframe and then heatsink -> lower RthJC -> higher power dissipation.
Higher current ratings, also due to more bondwires.
Big chip drawbacks:
More capacitance and charge storage, lower transition frequency (ie, slower).
More bulky expensive, bigger package, etc.
Along with that, power transistors usually have lowish hFe along with other undesirable characteristics that you have to live with, like lead inductance and collector capacitance to hetasink.
You can compare a high current small transistor like 2SC5706, with a big power transistor like MJL3281 or MJL21193, and pay attention to parameters influenced by chip size, like SOA, power, capacitance, fT, etc. Another thing is weight. The TO264 weighs 10 grams, and most of it is in the thick slab of copper just below the chip. The DPAK transistor weighs 0.3 grams. Thermal mass is important if you need high peak power dissipation.
So if you're thinking about amplification, a bigger die with the associated huge capacitance would be a drawback at medium to not so high frequencies.
The datasheets usually don't talk much about charge storage or other parameters that influence switching speed, unless the BJT is specifically sold for that use, but then why not use a MOSFET instead...