You might object that marriage in itself is an outdated/outmoded, and we should all live polyamorous lives. Marriage has been a relatively stable social/legal contract for millenia, and I think attempts to make it irrelevant or obsolete will always fail.
Perhaps other people from who is taken opportunity to have a relationship (and perceptive to have a family)?
To me, it seems it would accelerate the wealth gap we already see today.
Edit: Here is a good summary of some of the concerns I would personally see with a system. From the Supreme Court in British Columbia.
http://www.courts.gov.bc.ca/jdb-txt/SC/11/15/2011BCSC1588.ht...
Edit2: And frankly, I think I don't see the big upside that makes all those risks worth it.
My views regarding wealth distribution and the like would easily be associated with socialism and communism by many (Americans at least). But here my first reaction is more like sorry for you if you can not find a partner because of your social status. This worries me a bit because you could easily argue that a relationship and having children is in some sense more important for humans than being wealthy. I really have to think about it for some time.
The only thing I am already pretty sure is that there is nothing that justifies a right to have a relationship, i.e. there is no justification to force someone into a relationship with someone if for example this person is simply a really unpleasant person. But is it desirable to level the playing field as good as possible? I can't say ad hoc, but my intuition is no.