I'm a little confused by this. Are you saying it's better for a support to steal a kill instead of taking the assist (for assist streak) and letting the laner have the kill?
no, lemme try and explain it better
say you're killing someone, you roam mid and go try and kill their midlaner who has a 300g bounty. if you kill him 1v1 with no help, your team gets 300g, which all goes to you. if someone helps you kill him (say heals you or deals some damage), your team gets 450g, the kill money goes to the killer, and 50% of the kill money goes to the assister. now if you can't manage to just get an assist (say you're annie and can't do anything other than damage), it's not necessarily a bad decision to steal the kill so that someone gets that 150g extra gold that would be lost completely if there were no assists
obviously don't do it every time, but it's something to be considered. when a jungler comes mid and just flat out steals my kill, i'm not too mad (unless i was far behind) because i may not get that much money, but it puts my team more ahead than if i just gotten the kill myself. in some cases you might want not to do it say if there's a pretty big bounty you want to make sure your carries get. if i'm really behind in midlane, killing the other mid gets me 500g, i really need that money so maybe in that case don't steal the kill. or first blood or whatever.
assist streaks shouldn't really be affecting this, what they do is they offset the assist money split. if we split the 150g of a kill among 3 people, it's really not much money (basically two minions/ward kills). but if those people are constantly getting assists they get a little bonus so that you don't have to worry about "hey i'm getting an assist which means my teammates get less money", because all the people getting tons of assists always get flat bonus money.
it's kinda complicated, but general rule of thumb is the more assists the better, specially one is much better than zero
i bet scy could explain this with 1/5th number of words