No, it's nothing to do with balance.
We use delta for transmission because line plant is expensive and the lowest number of wires wins. For a 3-phase system that's 3 wires.
In theory we could use 3-wire delta for distribution to individual installations and some systems work like that, without a neutral at all. Each single-phase circuit is connected between two of the three lines. E.g. one load is connected between L1 and L2, another is connected L2 to L3 etc. There's no need for the loads to be balanced, if they are unbalanced the three line currents are simply different. Shipboard domestic power is often delta, historically it was popular in parts of Europe.
But for consumers, 3-phase 3-wire delta has drawbacks. Everything has to be double-pole switched and fused because both wires of a single-phase circuit are lines. More importantly, it misses out on an important advantage of 3-phase 4-wire which is that you can take power at one voltage L-N and a different voltage L-L according to application. E.g. with 3-phase 4-wire one supply can provide 230V single-phase power with the convenience and safety of an earthed neutral, and at the same time 400V 3-phase for industrial loads with the advantage of reducing the current by sqrt(3) saving on copper and losses. These advantages of the 3-phase 4-wire system come at the cost of providing four wires instead of three, and for installations of buildings that extra cost is well justified.
So we have standardised (at least in the UK and many countries) on 3-phase 3-wire for transmission on grounds of economy, and 3-phase 4-wire for distribution to normal consumers on grounds of flexibility. Hence, most local substation transformers are wound delta-star.