Possession is only good for preserving a lead. To shoot is to relinquish possession. Shooting is giving the ball away, hoping for a goal, but might as easily end up with the keeper saving (turnover), a goal kick (turnover), or a deflection or block (50/50 chance of a turnover).
If the players are coached to keep the ball, there's a certain amount of reluctance to shoot as shooting will concede possession unless a goal is scored. I think this is why possession-based teams try to walk the ball into the net, scared to shoot unless they have a perfect opportunity.
Swansea have been outshot a bunch of times this season by teams with nowhere near as much possession. I'd rather outshoot than out-possess the opponent every day of the week (the obvious caveat about quality of chances aside - and it's debateable that possession creates better chances. If anything it's the opposite, as opponents have more time to organise).
Logically, a possession-focussed team will not score as much as a team more willing to take risks. I'm willing to bet that if you took two evenly-matched teams, one with 80% possession and fewer than 10 shots per game and the other with less than 50% possession and 15-20 shots per game, the 15-20 shots team wins a lot more often.
The possession game was solved by the high-press over five years ago. It's outmoded. The big clubs can play possession and still score plenty because the quality of their players is significantly higher than most of their opponents. It's the talent gap producing those results, not possession, which they end up with almost by default because of that talent gap.
A non-elite team can only take possession so far. Even at the height of possession football, before the high-press, during Swansea's first Premier League season, the Swans were still the 6th lowest-scoring side in the division (15th overall) despite finishing 11th. Nostalgia aside, that team would be destroyed by the high-pressing teams of today.
I'd agree with the comments here regarding defensive player selection. I like Downes a lot, but if Grimes goes in January, Downes is there to take over. There's no reason to play both at the same time unless you're away to one of the better sides, and even then I'd throw caution to the wind and attack because it's more fun.
Patterson's hitting his stride and Piroe is the first legit #9 this team has had in years. I'd go 3-4-1-2 and give Piroe some company up top with Patterson or Ntcham behind. There's plenty of attacking talent in this team, but a tactical system based on ball-retention isn't compatible with attacking talent. These guys need to let loose more, work on fast transitions, balls into space, and getting quick shots away. Every sideways pass in the final third is 3 more seconds a defender has to get his breath back and get into position.
As the saying goes: don't bore us, get to the chorus.