I guess, to be simplistic, you could split it into four eras:
1. BR days until a couple of years into privatisation: HSTs providing everything north of Bedford (had been Peaks until ECML electrification etc freed up a few HSTs). Service from London to Nottingham/ Sheffield only every ninety minutes each, although I’ve seen people say that there were Leicester “shorts” to give a thirty minute service that far (I don’t remember those services, but then I’ve not lived South off a Sheffield so in guess they’d not have been on my radar). Services improved to hourly to both Nottingham and Sheffield by privatisation. Stopping patterns South of Leicester were pretty erratic, think of the ECML north of Newcastle where Morpeth/ Alnmouth/ Berwick/ Dunbar all have a reasonable drive to the big cities but you might struggle to get a train from (e.g.) Alnmouth to Berwick because most only few trains make multiple stops in between Newcastle and Edinburgh
2. National Express era: Two coach 170s introduced to provide an hourly service from London to each of Derby and Nottingham (with a token extension to Burton/ Matlock/ Barnsley). These Turbostars had a ten minute dwell at Leicester so that passengers could swap with the HST on the “adjacent” platform, to give a faster journey from Beeston/ Long Eaton to London, or from Sheffield/ Nottingham to Bedford/ Luton. The 170s picked up all stops South of Leicester, allowing HSTs to generally run non stop, speeding them up. I think that the 170s stopped at everywhere from Leicester to Bedford, with one stopping in central Luton whilst the other stopped at the Airport? Despite a two coach DMU that took two hours or more to get from London to Derby/ Nottingham not seeming very appealing by today’s standards (I say two hours , these trains stopped pretty much everywhere and had the long dwells at Leicester), they clearly demonstrated untapped demand on the neglected MML (which had always played second fiddle to the ECML/ WCML) and were extended to three coaches. Soon, this wasn’t enough so National Express ordered four coach DMUs to replace them, adding on some nine coach versions to turn order for a speculative hourly London - Leeds service. If the SRA (or whoever was nominally in charge on those days) has approved this, XC’s struggles to cope with demand from the midlands to Leeds would have been massively aided, maybe there’d have been some fare competition with GNER etc for London to Leeds fares, who knows.., one of those “what if” moments
3: New trains, new platforms, new operator, new route: a bit of a busy period as the 222s were delivered in 2004, London services were squeezed into the cramped platforms in the far north west of the station in 2006 to accommodate Eurostar in the main “shed”, Stagecoach replaced National Express in 2007, Corby was opened in 2009, the 222 fleet was rejigged quite a bit to balance out the “short” and “long” trains, the Hull Trains 222s were taken by EMT, it was a bit of a blur, the Long distance high speed fleet was now four/ five/ seven coach 222s plus some HSTs (as the St Pancras route has inherited HSTs from fleet upgrades on the ECML and later Operation Princess on XC, now they were able to use the 222 fleet to show some HSTs to go to GWML who needed additional diesel capacity). Both Sheffield services were generally 222s that ran non stop south of Leicester, both Nottingham trains stopped at Market Harbourough with the Nottingham “HST” path running non stop South of there and the “short 222” from Nottingham providing a roughly half hourly service at Bedford etc when combined with the new hourly Corby service. Corby was a mixed blessing for EMT, it allowed some other services to be speeded up but created a lopsided timetable and additional pressure at a cramped St Pancras
4. Now: the half hourly Corby EMUs allowed the slower Nottingham service to be speeded up, but the faster Nottingham train additionally stops at Kettering (for Corby connections).
So there’s never really been a clockface HST service from Luton/ Bedford to Nottingham/ Sheffield, the clockface pattern south of Leicester only really came about with the 170s, until the Turbostars came along the number of stops and distribution of stops was fairly random - the MML has always struggled to accommodate passengers at the stations between Bedford and Leicester, given the lack of Network South East (which ran to Northampton/ Leicester etc but didn’t provide a “local” service as far out of London when it came to the MML), just as it struggled with modern rolling stock (In BR days) and journey times (faster to get from London to York/ Leeds than to Sheffield). Slowing down long distance trains to try to tap into the Wellingborough - Sheffield market has never been much of a priority