It might not be strictly Marxist, but it’s an internally-consistent and relatively common viewpoint that people within a liberal democracy could be persuaded to vote so that it becomes a social democracy, then democratic socialism, and then keeps going all the way until it’s communism. I saw it on reddit, so there’s room for doubt, but I’ve read that Marx didn’t think this approach was impossible, just that the starting conditions were less common, and in the era he lived in, autocratic monarchies were the default, and no major countries (based on whatever definition Wikipedia uses) had universal suffrage (if you count women as people) until ten years after he was dead.
It isn’t necessarily internally consistent viewpoint. It is common, you’re correct, but such a theory requires at some point wresting political power from the Bourgeoisie, which to this point requires revolution. This is only affirmed by the experiences of comrade Allende in Chile, may he rest in peace. The fact that it is a common viewpoint among liberals and Social Democrats does not mean it is internally consistent, nor does it stand up to scrutiny. Time and time again has proven the fruitlessness of reformism, Rosa Luxemburg has been proven correct time and time again with respect to Reform or Revolution.
As for Marx, the concept of a theoretical transition along peaceful means wasn’t impossible, merely extremely difficult and might as well be, in the context of his time. Now that Capitalism has transformed into Imperialism globally, this is only further affirmed to be true as the State and Imperialist Capitalists are further and further bedfellows.
Historically, plenty of people have gained more rights through actions that were far short of an actual revolution. For example, it would be naive to say that the suffragette bombing campaign didn’t at the minimum accelerate when British women got the vote, but killing four people and wounding twenty-four isn’t a revolution, and women getting the vote moved political power to a group that previously had effectively none. Initially, the only women who had the right to vote were property owners or the wives of property owners, but the same act of parliament gave non-land-owning men the right to vote, so it was specifically transferring power from the Bourgeoisie to workers, too. Clearly, power can be transferred from the Bourgeoisie to workers through reform.
There’s a perfectly legitimate argument that there may or may not be a limit to how far this could go, e.g. whether there’s a threshold minimum amount of power the owning class can tolerate before further reform becomes impossible, or whether if it’s done in palatable increments, reform could continue indefinitely. It’s an unfalsifiable argument, so whether or not it’s true, the only way to know is if it’s done successfully, and until then, there’s a first time for everything might apply (although you could try and fail a whole bunch of times and end up with an upper bound on how easy it might be).
Personally, I think it’s a decent rule of thumb that if you’ve got enough people who agree on the same position to make a revolution successful, you’ve got enough people to get an equivalent government elected if you’re in a vaguely functional democracy. Taking over an existing party or forming a third party that dwarfs all the others should need about the same amount of the population as battling against an incumbent government and any other factions that want to be the last ones standing after a revolution. If you’re not in a democracy at all, then obviously a revolution is necessary, and sometimes a self-described democracy isn’t one or isn’t working properly, so needs some kind of push in the right direction, but if you’re already in a democracy, and not winning elections, a revolution’s likely to backfire, especially as the type of person most keen on using weapons against humans is the same type of person who’ll always put their own needs above the needs of others. Getting loads of people to agree with you is the biggest hurdle both for successful reform and successful revolution.
You’re confusing concessions with outright shifting the balance of power to the hands of the Workers. Giving women the right to vote is fantastic, but in the context of allowing the Proletariat to end Private Property, the scale of power transfer is on another scale entirely. That’s why I said at some point said scale must be tipped, and historically that has never happened without revolution.
The question of whether or not it’s even technically possible largely don’t matter at this point, we know revolution works and we know reform has never worked despite being tried far more for far longer.
Personally, I think it’s a decent rule of thumb that if you’ve got enough people who agree on the same position to make a revolution successful, you’ve got enough people to get an equivalent government elected if you’re in a vaguely functional democracy.
Why is this a rule of thumb if it’s never happened? Revolution has been the only way the scales have been tipped, because bourgeois democracy places firm limits on what is acceptable to be voted on. You’re correct that revolutions require mass popular support, but wrong that existing Bourgeois frameworks would allow it to begin with. Read the Luxemburg book.