I’d love to see some documentation from the '60’s where making the Klingons look more alien was actually discussed. A lot of production memos and such still exist. It’s not that the capability wasn’t there, (look at the Tellarites or the Andorians) but the expense of doing a large group of Klingons would have wreaked havoc with the budget.
I would imagine they changed them up for TMP because it looked cool. Ironic they had the money to populate the film with dozens of exotic aliens and most of it ended up on the cutting room floor. Robert Wise allegedly put all the Enterprise’s alien crewmembers in the Rec deck scene way in the back where they are barely visible. What was he thinking?
TNG tweaked the Romulan look enough that you have to wonder how Spock can walk around on Romulus unnoticed. 😉