As long as your name is on the deed for the house and since you do not live in a common law marriage state - I don't see any issues. You have sole ownership and would want to continue paying taxes and insurance - end of story.
As far as entering into a contract as to who pays for which bill - that sounds a bit over the top paranoid to me. The way I look at it, if you have so little trust in each other you are not ready to move in together.
There are a million ways to split and arrange things to suit both of your separate situations. Splitting everything down the middle and asking for X in rent is only fair if you both bring home the same amount of income, otherwise you need to find a different percentage split based on each other's income.
I'm in an over 20yr SO relationship and I contribute significantly more now than I did when I first moved in, because now I can. But I had to speak up for myself at the beginning, which wasn't an easy conversation for me:) because on the surface a 50% split sounds right and fair, but it isn't if it leaves one of you with next to nothing left over for the month. Once I explained where I stood and what I could contribute at that time we agreed on a suitable split.
You have to remember that things shift and change within a relationship, everything continually changes from your income to your opportunities to who is the stronger partner within your relationship at a particular time in your lives. If you can't even envision that your partner will be there for you in a time of crisis much less can be relied upon to actually pay the phone bill then ... well.
FWIW - we kept it all separate for several years but over time we added each other on our accounts and have a POD on each account, so if one of us dies the money in the account is automatically available to the survivor. (Without a POD the bank will not give you access even to a joint account.) We also made each other beneficiary of our investments and on everything else.
We've never had a single issue concerning bills or purchasing something new - we discuss it and decide together. If it's under 200-300 and it's just something only one of us is keen on having or doing then it just comes out of our individual accounts.