Wiring Lights with Independent switches
The original diagram has a problem

There's one issue with the original diagram -- it shows the two /2 NM cables between the lights being used in a way that can be considered a 300.3(B)/310.10(H) violation for cables in parallel.  So, as long as all the wires between the two lights are run in a single cable, you are fine in doing what you propose -- powering a light from the same circuit via two parallel paths is not a Code violation, or a major issue otherwise, as long as folks know to turn things off at the breaker before servicing the fixtures.

I would take up Chris Cudmore's suggestion of making the black always-hot and the red switched-hot, by the way, though.