Question: I know that in a transformer the power is conserved on both sides, and hence there's no power amplification as such. That's fine!

But if I instead want only a voltage amplification, then choosing proper turns ratio and connecting the load across the secondary would serve my purpose. So can you consider it as voltage amplifier? If yes, then why is it not used as one?

Answer: 
Only for ideal transformers, power is conserved.  

Real transformers have losses, which may be load dependent. So, in that case, the 'output' voltage is not the gain times the 'input' voltage. 

For voltage amplifiers, you also want them to have unlimited (or at least large) current supply. This unlimited current is needed, so the output is not dependent to the load, i.e. the voltage should not collapse because of the load.  

For transformers, this 'output' current is dependent and limited.
Amplifiers typically provide input-output isolation. Changes in output energy need not require more input energy (tho the VDD rail must support the output demands)

A transformer of course does not provide isolation.