This is a very old and tired complaint but Shaun really was the stupidest thing about fallout 4. The synths were pretty bad too but the synths weren't supposed to be the characters motivation for doing anything. Shaun was several jukes in a contrivance trench coat that clashed with...everything else, to be honest.

So anyway, some dumb ideas i came up with in ten minutes to replace the "Find your son" plot, still using the basic ideas

The SS is still pre-war, and still is the only survivor of Vault 111. This time, they're the ones taken by Kellogg, and after undergoing something (basically just being conscious in the Institute for a bit) before getting thrown back out into the Wasteland. The motivation is figuring out who those science guys were, what they wanted with you, and later, are you a synth?

The SS is not pre-war. Game starts with you traveling with some merc group (gunners maybe?) told to investigate Vault 111 and get out any survivors of the cryo chambers. You find the cryo'd people, but the Institute and Kellogg are right behind you. Kellogg kills everyone in your band, leaving only you, as you hide or play dead or whatever. The Institute takes all of the people you were supposed to save. Motivation is 1: avenging your team and killing Kellogg, 2: figuring out why you were sent to Vault 111 in the first place, and if this job was a set-up.

SS is a traveler who stumbles upon Garvey in Concord. You save him and his group, and can join the Minutemen as usual. If you accept, the Settlement radiant quests start to involve the Institute. Synths are constantly attacking your farms, you keep finding replacements in your settlements trying to kill the original people, and the Institute sends you letters requesting your cooperation or to disband the Minutemen, depending on your actions. Kellogg also keeps showing up and throwing wrenches in Minutemen business. Now, as the General, you're trying to find the Institute to make them stop fucking with your people. If you decline the Minutemen, the Institute starts attacking the major settlements, and now the Commonwealth is under invasion. The Brotherhood rolls in with no fake niceties, and you get roped into it by either the Railroad or BOS in a random encounter.

Back to Pre-war SS. The cryo chambers open after 200 years on their own, and all of the 'residents' stumble out to find the Vault staff dead. Someone has to go see what its like topside. You can volunteer, or everyone draws straws/flips a coin/etc and you lose, having to go up. You go find Codsworth, he tells you there are people in Concord. Find Garvey, etc etc. Vault 111 is now up and operational by Pre-war civilians, but you're tasking with getting supplies for them. Joining the Minutemen makes this easier, as you can send supply routes rather than do it yourself. The Vault interests the Institute, who send Kellogg to attack Sanctuary and the Vault after hitting a certain threshold of success. You go after the Institute once it looks like the Institute, before the war, had something to do with Vault 111, and are now trying to come collect those results. Motivation is figuring out what the Institute is actually planning for the Commonwealth, and why Vault 111 and its people seem to be their ticket to that future.