"The law has always placed a higher value upon human safety than upon mere rights in property."
Firstly, bait bikes are inevitably going to be cheap bikes. Thieves are more interested in expensive bikes - and if the expensive bikes are not only more profitable, but also safer to steal, then they're bound to step up their lock-picking and angle-grinding game.
Secondly, finding someone to organise this would be difficult. Any single organisation sufficiently large enough to do this would be bureaucratic enough to insist on the same make/model of bike (for the obvious homogeneity benefits), which would make them as obvious as an undercover Crown Vic. Conversely, any kind of grassroots or community effort would (by design) need to alert as many people as possible to the venture, including the bike thieves themselves - thus spoiling it before it even begins.
Finally, these things are chop-shopped almost the instant they get on-sold. Tearing a bike down can be done in a public park in 5 minutes flat with a pocket's worth of tools. The bike thieves can adapt a lot more easily than the sting operators.
There's no reason to assume tha bait bikes are going to be cheap bikes, nor that all bait bikes would be the same make and model.
I assumed cheap bikes because of Ainmats[1] ratio of 1 in 100 bikes being trap bikes. 1 in 100 in any reasonably-sized city means tens/hundreds of thousands of dollars of kit (including GPS), and anyone with that kind of scratch has someone trying to minimise expenditure. Or, why spring for a Trek Butterfly to catch a hungry junkie when a Huffy would net hundreds of the same?