The poskim write that before bentching one needs to remind himself of the churban. During the week we do so with "Al Naharos Bavel" [ANB]- which has more of a mourining theme and on Shabbos we do so with "Shiur Hamaalos" [SHM] which is more of a simcha theme.
So first of all as long as someone is saying one of them they are fulfilling the spirit of the law i.e. remembering the Beis Hamikdash and doing no wrong per se.
ANB is not said on days where we don't say tachnun, on the eve of days where we don't say tachnun and any other joyous occasion. So days where ANB could actually be said are somewhat limited.
The Piskei Tshuvos brings down in the name of the Rebbe of Liska and The Munkatcher Rav the SHM is always said. Unfortunatly he does not bring their reasons.
IMHO I have the feeling that in the first few generations after the Baal Shem Tov there was an intense focus on simcha and to keep away from any form of atzvos.
Even though we no longer have those spiritual levels as those chassidim had the minhag stuck. Again a personal opinion and I am trying to track down a source.
NOW as I understand -
ANB or SHM needs to be said ! it can't be skipped in favor of finishing 30 secs earlier
If one follows all chassidic customs than one should continue saying SHM during the weekdays.
If one does not have such customs than ANB should be said on the appropriate days before bentching and if they have said SHM until now then chalk it up to one of those things they learnt later in life and they should change.
We only need to look at the Dembiciner Rav ZT"L who changed from SHM to ANB in his later years and encouraged everyone to do the same.