No, you are incorrect. For a #1 overall draft pick, David Carr never had a winning season throughout all of his career, had more INTs than TDs and never was able to make his teammates better.
David Carr Among 8 Most Overrated Houston Texans in Franchise History
No. 2: David Carr, QB
David Carr was the first overall pick of the 2002 NFL draft. He was also the first pick in the history of the franchise, excluding the expansion draft.
Carr was expected to be the franchise quarterback, the guy who would lead the Texans offense for many years.
However, due to an extremely ineffective offensive line and Carr's own shortcomings as QB in the NFL, he was never successful. He never lead the Texans to a winning record, although this cannot be solely blamed on him, and he threw more interceptions (65) than touchdowns (59) as a starting quarterback for the Texans.
Carr was supposed to be the guy who would lead the expansion Texans to a bright future, but instead, he was the guy that gave them a dark, dark past.
https://syndication.bleacherreport....-houston-texans-in-franchise-history.amp.html
David Carr was ranked by NFL.com as #38 out of the 52 No. 1 Draft Picks in the common NFL era. That's pretty bad.
https://www.nfl.com/photos/ranking-all-52-no-1-picks-of-the-nfl-s-common-draft-era-0ap3000000797366
David Carr was also picked among the worst draft picks in Texans history.
https://www.nfl.com/news/houston-texans-best-and-worst-draft-picks-0ap1000000162231
David Carr's career record was 22 - 53, albeit not helped with a better Oline and better talent around him, but he was let go by the Texans after his 5th year. David Carr spent the rest of his career as a backup QB for 4 other teams. Horrible for a #1 overall draft pick.