Some interesting points made here. I'm of the same mind as you OP (although I wouldn't call marriage 'just a piece of paper', but I do see where you are coming from. DP and I are unmarried, in our 30s, and have one DD.
We co-own a property, which has been placed 'in trust' - if one of us dies before the other, the mortgage will be paid off by the insurance, and the whole property passes to the surviving partner. So no problems with the inheritance of property.
We have drawn up papers with a lawyer naming each other as next of kin, so in theory we have the rights to turn off each other's life support machines, etc.
DP has parental rights over DD as he is named as father on her birth certificate.
DP's life insurance policy (paid for by his company) allows me to be named as beneficiary.
If one person is going to be a SAHP I can see the benefits of being married, but that is not our situation.
The ONLY possible benefit that I can see from getting married is that DP earns far more than me and has a much better pension. However, this is because I have chosen to work in a more 'exciting' industry than DP where the pay is correspondingly lower, so being the lower earning partner is a situation that I have freely chosen. I feel that (as a feminist) it is my own responsibility to provide for myself.
Finally, I think that Sue Bridehead quote nails it for me - I hate being told what to do, so worry that marriage might actually weaken our relationship. (Although given what happen to Sue, Jude and their children she may not be the best person to take advice from....)