There may be other downsides, but the one that immediately comes to mind is that some of your client's devices may well be extremely resource constrained. The obvious type of device that comes to mind is mobile phones but there's also set top boxes and many other non-full-blown-PC web clients around.
What ever work factor downtuning you need to do to conserve server resources may well be dwarfed by the downtuning you need to do to get bcrypt to run in a reasonable amount of time on a mid range smartphone.
Is this still true? I see some articles suggesting it from around the time that Android 2.1 or lower was a "mid range" smartphone.
It doesn't seem like it ought to be true. Running bcrypt in Ruby with default settings takes small fractions of a second on a few-years-old Macbook Pro. Even if the smartphone is 100x slower, it should be within the realm of reason to run a process that might take 1-2s once every thirty minutes or so.
Now, I'll buy that if your target device is not a mid-range smartphone, but "the very bottom of the smartphone market," bcrypt might be too expensive.
What ever work factor downtuning you need to do to conserve server resources may well be dwarfed by the downtuning you need to do to get bcrypt to run in a reasonable amount of time on a mid range smartphone.