Of course, if you believe that British agents killed Mr. L, you could argue that they chose to use Po210 on the assumptions that:

A. It would be mistaken for thallium poisoning (which it was, for a few weeks), while also...
B. Killing with more certainty than thallium (there's a fairly effective treatment for Tl poisoning, quite a few victims have successfully recovered, and Litvinenko was said to be in robust physical health -- so there's a good chance that thallium would have failed to kill him)

But if plan was indeed to kill him with polonium but make it look like thallium, then things backfired rather expensively when the Po210 was detected, which ultimately cost the UK government a few million pounds in decontamination efforts and laboratory tests for hundreds of people. (Fortunately, it appears that fewer than 20 people suffered a level of polonium exposure that MIGHT MAYBE POSSIBLY raise their risk of developing cancer during the next two decades.)