Yes, I'm afraid this is correct.
The new county judge (Lina Hidalgo) is generally anti-car and anti-road. Several months ago there was a Harris County Commissioners Court agenda item to study shelving or canceling the project. That's probably a necessary formality since they've already spent a lot on this project, I'm thinking at least $100 million.
With HCTRA's revenue expected to drop significantly this year, Hidalgo has a good excuse to drop the project. To add insult to injury, this week Commissioners Court voted to divert $300 million out of HCTRA immediately and then $90 million per year to non-transportation budgets. It's the new reality with a democrat-controlled Commissioner's court. While a few previous commitments like the 225/8 interchange will be honored, I think we're seeing the end of expansion of the Harris County Toll Road system. HCTRA was managed financially conservatively for a long time, and the new majority is looking to harvest that money for non-HCTRA purposes.
https://www.houstonchronicle.com/news/houston-texas/houston/article/Harris-County-may-create-corporation-to-free-up-15569039.php
Is it permanently dead? It's hard to say. If republicans regain control it would likely be revived, but that seems unlikely given demographic trends.
That is why NTTA is a multi-jusisdictional authority. While one group could make major changes in whom they send to the authority, the single or perhaps a couple of votes do not kill everything.
Every county in Texas has exactly 4 commissioners and a single County Judge (Presiding officer of the Commissioners' Court; the legislative body of the county.) One vote swing and everything can change. The legislature can and probably should force the county to divest itself of the total overall authority over the HCTRA. There would probably still be a few hiccups, but it could be done.
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Would the toll road extension have been a "crucial" link in the Houston roadway system? After all, the Interstate 69/US 59 freeway is just to the east of where the HTR extension would have been.
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The I-69 / US59 Freeway is not new by any stretch of the imagination. While the I-69 designation is new; this has been an ever expanding freeway since the seventies or farther back. By pointing out what I mean is that this does not enhance capacity so as to make the Hardy Toll Road unneeded.
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Well that just sucks ass. I thought judges weren’t supposed to be biased.

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The County Judge is PRIMARILY the presiding officer of the "Commissioners' Court" ; the legislative body of each Texas County. In smaller counties, the County Judge also presides over the County Court at Law. This Court hears the probate, family court issues (sometimes), and State Jail Felonies (as opposed to State Prison Felonies which are heard in District Court). I am relatively sure there is a SEPARATE County Court at Law in Harris County. This would make her a Judge in title only.