Forgoing an entire combat round to "prepare" an assassinate attempt would probably be a relatively balanced house rule. Most fourth edition lurker monsters do exactly that, and they're not overpowered or anything.
It would generally be crappy.
So there is a core problem with the 5e rogue in that it is hard to optimize.
Multi-tap characters scale with damage additions to each tap in a nice way. Give a character +17 to damage per tap, and 5 taps, and they gain +85 damage. Do the same to the rogue ... they gain +17 damage. 34 if the rogue dual wields.
It deals very decent damage in a single-class, magic-item-less game with no feats. But each addition to the game erodes its relative damage.
One way you can deal competitive damage with a rogue is by getting a second sneak attack each turn; exploit the reaction. This, however, isn't generally dependent on feats, magic items or multiclassing. Well, the Scimitar of Speed; gives you a bonus action attack that you can use while you ready your main action attack to go off on someone else's turn and get a 2nd tap of sneak attack damage.
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You can compare various rogue archtypes. The Thief has nothing mainly useful in combat until level 17, where it gets 2 turns on the first round of combat; that is way better than the Assassin 3rd level feature. Its 17th level feature also requires surprise, but when stacked does decent damage.
If I was to fix the Assassin, I'd fold 7 and 13 level feature together and add a new not-mainly-combat one in there. Maybe poison crafting related.
Death Strike, at 17, could also be improved.
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Assassinate could probably be extended to "on a target who is surprised, or who you have been hidden from for the entire combat up to this point". That permits some janky stuff, and also means that you aren't completely destroyed by your party not letting you open the gates of battle every fight.