Any point to claiming depreciation on sold rental property?

You're required to claim depreciation. Well, not really. But if you don't, you have to pay a recapture tax as if you had.

It's a good idea to fill it out because on form 4797 IRS expects you to list depreciation you could have taken. If you leave depreciation off all forms maybe it will not make a difference, but the IRS computers might flag it and send you a letter.

Also, depreciation lowers your income, so if you're in the 28% or higher tax bracket, you save 28%. When you recapture your depreciation it's at a lower rate, I think 15% but possibly 25%. I don't think it would be 25% since this applies to appliances (1250 property, 1245 property, not sure which).

It can make a difference. It won't affect the total gain, but it may shift from of that gain from capital to ordinary income treatment. Even though the depreciation deduction would cancel against the additional ordinary income recognized, it does affect the tax computation. I think that in most cases, it will lower your overall tax in an amount equal to the depreciation times the marginal capital gains tax rate.

Yes, it has an effect, but not what you stated.

Then what is the effect/mechanism? My understanding is that depreciation lowers your cost basis, so you may think of it as being recaptured at the capital gains tax rate of 15% (or lower if your tax bracket is lower). Depreciation in excess of straight line is recaptured at higher rates, but property purchased relatively recently only allows straight line depreciation.

Answered before asked. Read what I wrote. I stated the effect in my first paragraph.