It really comes down to Judgement. Remember that it's always better to take the kill than risk the enemy getting away, no matter who says what.
Supports are inclined to give kills to their allies (especially their ally) but kills equate to 300 extra gold and of course, gold to anyone who assists you (100 divided by participants) that doesn't include Shutdowns (which of course, offer more) however, even in the scenario where you are a tank, you can always buy more tank items. You know what you can't buy?
Opportunity.
You cannot purchase any individual item that will definitively say 'This enemy can no longer contribute to the game.' there is no Stun, no Silence, no Blind, no Effect that will keep an enemy occupied more than being dead. While an enemy at low health will be inclined to recall (which usually means they'll need to regenerate lost health/mana) it means when they are done healing, they will return to the fight immediately after. After five minutes, recalling and healing takes less time than respawning does.
When an opponent is dead, you gain Pressure. This Pressure can be exerted in varying ways depending on your health and how much you have available to you. In most cases, this just means pushing the tower for a bit, and sometimes you are also at low health and need to leave lane to recover, but in some cases you can pressure objectives such as towers that are low on health, Dragons, Rift Herald, and maybe Baron. Remember that if your team has more members alive, you generally can exert greater pressure. This goes double if they lose a member that's winning their lane or their Jungler.
And sure, it's nice when your carry can get the Kill, which equates to them getting even more gold so they can buy items and be effective, but even if they get an Assist, that's still 100g in their pocket and you meanwhile, have more Pressure until that opponent has returned to the area being contested. If there is any doubt the enemy might survive, take the kill.
Sure, I'm Bronze, but I realize it's much more important the enemy is dead than who got the kill.