Bellamy is better than 75% of the players you mentioned there, he should start if he went to pool.
Is he a better winger than Downing? Nope. Is he a better centre forward than Carroll? Nope. And he's simply not better than either Suarez or Kuyt (who's not certain to start on the right himself anyway).
He's a decent all round attacker who can do a job covering the front 4 positions but he's not better on an individual basis to the players above and the role they play in the side.
Bellamy's entire career has been very inconsistent; he's had seasons where he's been very good and then had seasons where he's done nothing. At 32 now, he's unlikely to play to the levels of 2(?) seasons ago (probably his best season of his career).