Why do we need transforms (Fourier, Laplace, Z and wavelet etc.) for a signal to analyse?
No, transforms aren't "necessary", but they do make some types of calculations much simpler and more convenient.

It is possible to do all computation and analisys of a signal in either the time domain or the frequency domain.  However, some operations are much simpler and more intuitive in one than the other.

This can be illustrated with something as simple as a R-C low pass filter.  If it is on the input of a signal that you are measuring, then you may want to know how long of a delay it adds for the result to settle within some error of the input signal.  That is best done in the time domain by writing the equation of the output signal in response to a unit step input.  This could be done in frequency space, but would be quite convoluted, and you'd have to express some of the things you inherently know in the time domain in the frequency space.

On the other hand, if this is a audio application, you may want to know how the filter effects the amplitude of different frequencies.  That is most easily and intuitively done by expressing the filter in frequency space.  The response to any particular sine input could be computed in the time domain, but it would take much more computation and not be as intuitive.

In summary, both time domain and frequency space are whole and consistant ways of looking at a signal, but each gives different intuitive insights, and each makes different types of problems harder or easier.