Unless you are reviving a downed character, in combat single target healing is a poor use of the action economy. It's bad, even on a bladesinger. On a normal squishy wizard it's even worse. In an emergency, when there is absolutely no one else, a potion, healer's kit or goodberry is a better option. At my table, every character who is not a healer carries one of these - it's not a great expense since it is very rarely needed.
Now, if the spell gained was Healing Word, that would be a different kettle of fish...
I agree, but that is what we are talking about, bringing back a downed character. I wouldn't use it for anything else unless it was as I said right before a rest and was going to go to waste anyway.
That is what healing word is best used for too, bringing back a downed character, it to is mostly a waste for anything else in combat. It is better than cure wounds for this because it is V only, it has a range and is a bonus action. The only disadvantage it has is you can't ready it. The difference in hps is not relevant enough to matter.
Preemptive healing is generally not a good idea in combat unless you cast a high level spell that gives out a bunch of hps. It is almost always better to wait until someone is down then cast it unless you give them so many hit points that they will last several turns. It costs one action regardless, but the net hit point gain is better if they are at 0 then if you cast it before they are at 0 because excess hit points do not get subtracted on a hit.
For example if a guy is at 1 and you heal him for 7 then he is at 8, then if he gets hit the next turn for 10 he is down anyway at 0. You wasted your spell and action because he woudl be at 0 even if you didn't use it. If instead you cast your spell on the next turn when he was at 0 it would bring him back to 7. This is even true if he is hit and does not go to 0. If you let him get hit and taken to 0 before casting he will always have as many or more than if you cast it before he was at 0. If the initiative is such that you don't want to do this then ready your spell for when he is hit. Wait for him to go to 0 then put your spell on him to bring him back to 7.
For example, let's say you are fighting an iron golem your fighter is at 1 hit point and has a high total, say 60. If you cast a 1st level healing spell on him every turn it is not possible for the golem to kill him RAW. The Golem can take him to zero every turn, make a second multiattack with advantage for a failed death save every turn but he is still alive. Then you bring him back up next turn, and erase his failed death save. Even if the fighter goes after the golem in initiative, provided he does not have a failed death save already you can still ready your healing, then you bring him back up right after the Golem's turn and the fighter gets a full attack routine before going down again. Rinse and repeat. As an extreme example you can cast goodberry and then feed him a goodberry every turn after he goes down and for the cost of a single 1st level slot the golem can not kill him for at least 10 turns. That may seem cheesy but it is RAW.
As far as a bladesinger specifically, I would not use it in combat for anything other than reviving an ally. The only "healing" spell I use in combat with any of the bladesingers I have played is false life, and that is usually upcast using a 4th-6th level slot while I already have full hit points or very near full hit points and while I have used it in combat, it is usually cast before combat. She also upcasts false life on allys, and does this more often in combat than casting it on herself, but again it is usually when they are at or near full hps already and it is usually upcast at 3-6th level.