Difference between Analog IQ sampling and creating IQ digitally
You're right.  Whenever you can do things digitally you should because of all the advantages that you've listed.  But a long time ago it was expensive to do those low pass filters digitally.  If the LPF required is narrow (and requires a steep roll off), it would require many taps (multipliers) and they might require many bits so as to not lose precision to numerical accuracy issues. You also have to have the ADC twice as fast in the all digital case.
The disadvantages of doing the things in the analog realm are many though.  You would have to carefully tune LPFs to have the same group delay.  There could be many calibration issues.
Here's a paper describing a Hilbert Transform design