Can I generate pure sine wave with just a clock and amplifier?
Yes, you could in theory start with a sine signal and amplify it to make a inverter.  The result would be rather inefficient though.  The amplifier has to work with lots of signals, whereas you know exactly the signal you want.  The general amplifier approach ignores this and therefore doesn't avail itself of optimizations that would not be valid for amplifying general signals.

If you used a efficient class D amplifier, then the result might not be too bad.  One way of looking at a sine wave inverter is as a class D amplifier, except that it also synthesizes the signal directly instead of having to faithfully follow some analog input signal.

One important optimization that the general amplifier approach is missing is that distortion can be much higher for a inverter.  A few percent is a lot for a amplifier, but not much at all for a power cycle.

Also look at what amplifiers cost that can put out the voltage and power you want a inverter to put out.