It's not uncommon for someone to do something famous militarily and and get recognition politically. A recent real-life example would John McCain, a navy airman who was shot down over Vietnam and spent years in deplorable conditions as a prisoner of war. He would serve in Congress from 1982 until his death in 2018. He even ran for US President.
Picard was nearly killed by a Nausicaan, which made him a bit more willing to take some calcuated risks that paid off well. Q himself detailed the ramifications of that in the TNG episode Tapestry
The Jean-Luc Picard you wanted to be, the one who did not fight the Nausicaan, had quite a different career from the one you remember. That Picard never had a brush with death... never came face to face with his own mortality... never realized how fragile life is... how important each moment can be... so his life never came into focus. He drifted through much of his career, with no plan or agenda... going from one assignment to the next, never seizing the opportunities that presented themselves...
He didn't lead the Away Team on Milika Three to save that ambassador... he didn't take charge of the Stargazer's Bridge when its Captain was killed... and no one ever offered him a command.
He learned to play it safe. And he never, ever got noticed by anyone.
Picard was promoted (ostensibly two ranks or more) to Captain of the Stargazer after assuming command when the captain (and possibly the first officer) were killed (the event has never been detailed, but was mentioned more than once in TNG). Picard would command the Stargazer for 22 years.
Picard being offered the Enterprise-D (a brand new ship that was also a new model) was Starfleet honoring a man whose career reflected well on Starfleet. This was alluded to in The Drumhead, when Admiral Satie (who has been increasingly conspiratorial in her investigations) decides to question Picard in front of an Admiral and says
I've brought down bigger men than you, Picard!
You wouldn't say that to a nobody. The Cardassians went to great lengths to capture Picard in Chain of Command, going so far as to design a ruse that would require Starfleet to send Picard personally, as he had expertise in the area they built the ruse around.
In the Picard series, we see that Picard himself (now an admiral) tried to get an ambitious rescue armada for the imperiled Romulan Empire. That plan only failed because
synths attacked the Mars Colony and destroyed the fleet.
As we see later, that would be the end of Picard's ability to ride on his fame alone.