Despite all the uncensured content here in the comments, I'd like to answer my own question.
I understand that some have difficulties understanding the intuition behind the dilema here. I'll explain this first:
When we have deltas and we do Fourier to them, intuition says since we do scaling to a shifted delta function's time we might maybe somehow exchange a shifting operation on a scaling operation.
$\delta(t-t_0)$ can be scalled in time and since we have y=infinity at $t_0$ and the width of delta is infinitely small, then maybe we could make a little trick in future use?
Well then, wrong.
The thing is that when we do time scalling, the shift moves, that's right. But the time scalles as well. When we have $\delta(a(t-t_0))$ function, it might yield "the same" in time domain, but it's different.
The thing is that while doing fourier to it, since we have an integral during Fourier process, time scalling to delta function will have an impact on the integral and so that:
$\int\delta(a(t-t_0))= {1 \over a}\int\delta(t-t_0)$
Means that we have no way doing time scalling instead of shifting to delta functions despite appealing as much as it can seem to be.