Why is the effective base resistance important for the voltage divider BJT amplifier?
Everything is constant irrespective of the value of Rth. Isn’t it?


Nope.

That \$\mathrm{R_{in}}\$ depends on the transistor \$\beta\$ (\$\mathrm{H_{FE}}\$, whatever), and \$\beta\$ varies a lot from transistor to transistor, as well as varying somewhat with temperature*.

So you want the bias network to be "stiff" so that your lovely circuit that works in the lab with a few transistors that all happen to come from the same batch will still work in production when many transistors are being purchased from different companies, and possibly different transistor part numbers are being substituted, or the inevitable process changes are being made at the various manufacturers.

* I just realized I don't know how much -- hmm; something I need to learn!