Well, there are several issues.
1. Picard was always more of a diplomat who tried to talk his way out of situations and only resorted to force as a very last resort. Maybe that was the intention in the films, but if so then it was poorly executed.
2. There are already TWO characters on the Enterprise who fit the "action hero" model better than Picard, Riker and Worf. If Nemesis had been written competently, then instead of Picard going to duel Shinzon for some vague "I need to do it myself" reason, it should have been Worf. You know, the experienced Klingon warrior who loves to fight and is perfectly willing to die in battle if necessary.
3. Seeing a 60+ year old man with a artificial heart doing Rambo-style action scenes just didn't look right, especially with Riker and Worf around.
4. It just wasn't as interesting as his portrayal in the TV show.
5. They essentially turned him into Kirk, when he was specifically designed to be different from Kirk.
To be far on NEMESIS, the movie does give a reasonable explanation for why Riker doesn't go down there to fight Shinzon: he's got his *own* 'revenge' story, and he takes on the Viceroy. Admittedly it's such a damp squib it's easy to see why people forget it, but still, script writer John Logan had his bases covered on that one.
Worf, though? Not so much. I'll give you that.
INSURRECTION should really have been Picard's big chance to not be an action hero for a change. The script was weighed more towards philosophical debate anyway, and that one should have ended with Picard reasoning with Ru'afo, and convincing him with words
to put down his arms, and take up residency with his old people once more.
Instead, we got yet another scene of Picard fighting a guy like he's Bruce Willis or something, and then leaving Ru'afo to burn to death while he gets beamed safely away.
But then, I think fans would still kvetch on the internet about how 'Picard talking to a guy is a weak ending for a movie'. So what could they do? They would be damned if they did, and they would be damned if they didn't.