The ugly face of first order RC filter

In digital radio transmitter, the baseband waveform needed to be filtered, need to be lowpass filtered, because the bandwidth of a rectangular pulse is infinite and modulating an carrier with an infinite bandwidth baseband waveform producing infinite bandwidth signal, that cause interference to near channels. 

The first order RC filter, which is the simplest lowpass filter, and we using it just everywhere. It has cut-off frequency at fc = 1/(2piRC), but it roll-off at -20dB per decade which is very gentle, so it actually not "cut-off" after fc, it just slowly taking out the high frequency component inside a signal.

But now what make me even more frustrated, is the response of first order RC filter, in time domain.

First order RC Filter ! Why you are NONLINEAR PHASE ?

The pulse became asymmetric, it jump rapidly in beginning and settle slowly at the end, and the long tail extended to next symbol, that means some energy is leaked to the next symbol, sometime we call it Inter Symbol Interference - A bad guy. The problem of asymmetric waveform is caused by unequal delay of different frequency component inside the rectangular pulse, with lower frequency delay more and high frequency exit faster, textbook call it nonlinear phase, I call it ugly.

It's wont work, something have to be done.