We're already at the point where reliably spending the distributions involves prohibitive transaction fees. For someone with one seat the latest distribution is 0.00018967. The standard transaction fee is 0.0001 per KB and pulling the output of a transaction into a new one takes about 1/4 a KB. So spending the distributions will cost roughly 12%.
I disagree with this logic and I see this as the reason why dust is considered so evil. It is not. The main problem is bitcoin clients do not handle dust correctly. This is why I modify my bitcoind to handle dust without problems. I have communicated these changes
to Bitcoin devs.
Your solution only works when the dust coins are a small part of the value, but you have some bigger coins to spend. If someone is getting their coins by receiving small distributions from Nasty Fans, modest-hashrate pool payouts, etc. their entire wallet will be "dust"
Also, I'm not sure if this is a solution long term. There is an actual cost per KB to miners of including transactions (that is vaguely close to the current fees). Your suggestion increases their actual (average) cost per KB, so fees in that case would probably go up.
Another suggestion. Offer the option to take (small) distributions in a lower-value altcoin.