The lack of construction is mostly to do with most major US cities just not allowing enough construction. You can see the contrast with the handful of places like Austin that do allow construction, where rents have consistently dropped year-to-year even though the population has increased significantly.
There are a lot of counties that also use construction permits and inspection requirements as a source of income and charge absurd fees for it, on top of being slow and unpredictable even if you do pay. And a slow inspector or slow permit approval also costs money in the form of builder's and laborer's time that you get charged for as they sit around waiting for someone else to arrive.
I don't think construction has nearly as much relevance for Austin as you might think. Speaking as a former Austin resident, I left Austin in 2022 because rent highly spiked and I was effectively priced out of where I was staying (my rent spiked in the realm of 40%).
Rent has been cooling off in Austin because the amount of people moving there has heavily gone down and tech companies have either stopped opening new buildings there or have outright started to leave. The huge rise in rents was effectively due to a 'tech speculation' bubble as a result of every major tech company saying they were going to move to Austin and it was going to be the new tech capital of the US.
This. It’s NIMBY politics at the local level. Go to your county/city board meetings and ask for plans.