A heavy tunnel is not out of the question. It has been proposed before by SPT back in the 80s/90s, and has been included as a concept in a variety of transport planning documents since devolution.
Unlike Edinburgh, Glasgow isn't really on the way to any other city. While the ECML logically passes through Edinburgh between Newcastle and Aberdeen, Glasgow is quite out on a limb. If you do want to go from the WCML up to Stirling, Perth and onwards, you would go via Coatbridge. By the time you've gone into Glasgow city centre, you've added enough time to a long distance journey for it not to be worthwhile.
Accordingly, the plans for a tunnel revolve around suburban and regional trains. Glasgow has plenty of them, heading into both Queen Street and Central high level stations. Usefully enough, after EGIP there won't be much of a technical distinction between these services, as they'll both be run with 100mph 23m 6-8 carriage EMUs with doors at 1/3, 2/3 positions. A tunnel just wouldn't work without one type of train being able to run services on either side of the river, since there's no space to run extra trains.
The primary justification moving forward for a tunnel is that it can relieve both high level stations at once, without having any negative impact on passengers. Alternative heavy rail schemes like Glasgow Crossrail all involve some amount of disadvantage, with connections being lost and stations further from the places where people want to go. Central HL can plausibly see extra trains being run with new surface infrastructure (i.e. new platforms or tracks over the Clyde) but there's nothing that can really be done for Queen Street. My ever-favourite plan to dump tram-trains on Glasgow can only take 2 trains an hour out of Queen Street HL - maybe enough for 2030, but not enough for 2100.
A heavy rail tunnel would be one big investment for railways in Scotland. It would be of comparable scale and importance to the Queensferry Crossing, so it should be perfectly feasible for the Scottish Government to fund and organise it. Like the Queensferry Crossing, it will have an impact well beyond the local area. I've pointed out a few times before that there really aren't many trains across Scotland which don't end up at Central, Queen Street or Waverley. Adding extra trains between Inverness and Perth, or Aberdeen and Dundee, quite often depends on being able to run them all the way down to the Central Belt. If Edinburgh's too full, and people want to head down to Glasgow, then capacity in and out of Queen Street is going to be very relevant.