Am fairly sure I recall HSTs calling there - seems like a recent thing but was probably over 30 years ago
HSTs did call there, or rather, one up (late evening) and one down (morning, something around 09.00 IIRC) a day called. This was early 90s.
This was a 'remaindered' service - kind of left over from the days of the 45s+7 Mk1s. Originally - taking the 1966 timetable (following WCML electrification) the MML semi-fasts did not call at St Albans. (At least not in general, there may have been the odd one that did.) As the post by Peter Masson cites, somewhere around 1970 or perhaps 71, BR decided to introduce regular stops there for the semi-fasts, except in peak hours - so around 1615 - 18.30 or so, most down semi-fasts were first stop Bedford after St Pancras.
EDIT - I've just looked up the service for summer 1996. By then, not only had the St Albans stop been dropped, St Albans itself no longer appeared as a station in Table 53.
AIRI, both St Albans and Harpenden used to appear in the old BR timetable, even though no Inter-City trains ever stopped at the latter station. It was just considered important enough to show connecting trains.
I think the real reason for introducing the stop was poor loadings: yes, they wanted to improve the St Albans-St Pancras service, but in general the semi-fasts loaded poorly outside the peaks.
I have a memory of reading a very positive article in Rail News maybe six months after the stops were introduced saying how popular the new service was with St Albans' passengers.
I didn't follow changes in the 80s, but after Thameslink, and, I suspect, a combination of improved loadings on the semi-fasts during the day, plus the need to accelerate services where possible, the St Albans stops were discontinued - bar the one train each way. I think this lasted into the mid-90s.
I think this was fully justified, but, I do wonder if there is justification of what might be called "granny stops" * at places like St Albans and Huntingdon (which suffered a similar decline in Inter-City services). What I mean is, say, two up and two down Inter-City services stopping morning and afternoon could be justified in order to win those people who simply do not like/fear changing trains, but who could be tempted onto rail if only there were just a minimal service offered.
I suspect, however, that with privatisation, the TOCs involved are not interested in chasing any such small returns (if they exist) even if the timetabling/pathing issues could be solved for such odd calls.
* Of course, it would be a marketing disaster to call them 'granny stops' - this is just my term for the idea. And in view of the current thread about the Canadian comedienne, surely invalids (I'll call people that, I don't know what the current PC term is) would surely find such trains useful.