I'm torn on the .22lr as a SD round. It can do the job and having a gun, even a .22lr, is better than not having a gun.
With that said, while .22lr ammo is generally cheaper than all other handgun ammo, there is no real reason to carry a .22lr for SD. There are are ton of so called mouse guns out there chambered in .25, .32, .380 and even 9mm (granted, .25, .32 and .380 has failings too as generally accepted SD rounds).
With so many choices in small easily concealed guns, I can't think why anyone would pick a .22lr as SD round. Granted, for people that are recoil shy, it's a good option and again, its better than nothing. However, if you are going to bother to carry a gun, carry a gun that gives you the best chance of survival. You want a round that is going to open up as big a hole as possible and I don't thnk, all things being equal, a .22lr does that.
If a .22lr is all you can afford or all that you can physically shoot, buy all means carry one. If you can handle something with more recoil and have the cash flow, bigger is better.
Now, I'll also confess that the smallest SD round I carry is a .380 and that is not without its critics either but in the very least carry something that is reliable and accurate and you are confortable with.