Never again I shall propose such a bad idea. I swear.
Some of the responses here were quite harsh, and I think your post, as opposed to many similar posts, deserves credit for identifying and addressing some of the issues.
But the point remains. There isn't much of an upside, there is absolutely no problem with coins that are lost. Recycling certainly does hurt many, many ways of using Bitcoin (think for example about Casascius physical bitcoins, or wedding rings with a private key).
More importantly, even if the modification was advantageous at face value (and could be used in an alt), the economics of Bitcoin must never be changed, as that would destroy the Schelling point "the economics of Bitcoin will never be changed" which is the source of the confidence in Bitcoin investments. While more benign than relaxing the 21M cap, destroying bitcoins and creating new ones to replace them is certainly an economic change, and is thus ruled out.
And this is also a good opportunity to point out that the technical means to achieve the economic principles are fair game, and must change as needed if Bitcoin is to succeed.