Completely false. In Miami, Bron spent significant time off-ball in effective sets.
grantland.com
I don't have stats for before 2014, but in 2014 he only averaged 5.5 seconds with the ball per possession, 32nd in the league and only slightly more than Wade (3.7) or Chalmers (4.7). Time per touch was even less, he doesn't make the top-50:
A table featuring touches information for each player in the league based on selected filters.
www.nba.com
In 2012 and 2013 when Wade wasn't as
as he was in 2014, the time of possession for LeBron would have been even less.
In Cleveland 2015 he held the ball a little more, but was still just 20th in the league at 6.5 seconds per possession, the exact same as Kyrie.
A table featuring touches information for each player in the league based on selected filters.
www.nba.com
By 2016, he was down to 5.3 seconds/possession, a full second less than Kyrie:
A table featuring touches information for each player in the league based on selected filters.
www.nba.com
After Kyrie left in 2018 and there was no one to trust with the Ball, LeBron went up to 6.7 seconds/possession, 10th in the league but still nowhere near the real dominant ballhandlers like Westbrook, Harden, Wall, Lillard, and Kemba (7.8 to 9.1 seconds/possession).
A table featuring touches information for each player in the league based on selected filters.
www.nba.com
The most that Bron even held the ball was when he became the full-time point guard in 2020, leading the league in assists. He averaged 7.4 seconds/possession that year, 6th in the league but still fewer than Trae, Luka, Dame, Harden, and Graham (8.2 to 9.1 seconds).
A table featuring touches information for each player in the league based on selected filters.
www.nba.com
Which coach's offensive system was he failing to run?
Heat had a terrible offensive strategy in 2011, but that was partly personnel (Heat had zero three-point shooters in the starting lineup) and partly coaching inexperience (Spo hadn't come up with anything better than Bron/Wade taking turns). Through 2012-2014, Spo improved and Bron ran the system extremely well.