Whilst I do agree with what some PP have said above about legal protection etc, I agree with the OP -yes you may not have a share in the equity etc, but not paying anything at all? Where in the world would you ever be able to live anywhere for free?
When DH and I first started dating, he owned a one-bed flat, and I rented a one-bed flat. (His mortgage was £480 a month + £170 service charge a month = £650). I was renting for £750 a month. Between us, we were spending £1400 for our places (we both had bills on top of that), but we were only using one of them - we were spending 7 nights a week together (at mine, as I had pets).
Eventually, my landlord gave me notice, and I was stressed trying to find somewhere else to live, with pets. He sat me down, and suggested I move in with him (we were spending all our time together anyway). We did have a chat about finances - everything was brought up, including the equity etc. He assured me he would never just throw me out, if we broke up, without somewhere else to go, but to be honest, I guess I never had that security.
I ended up paying half of everything - £325 for half the mortgage, and service charge (a lot less than my £750 rent), and half the bills. I can't remember what the bills cost now, but even with them, I was still paying less than what I had been paying in rent alone. I guess you could say that my security was the extra money that I was able to save, and so had savings if I needed to find somewhere quickly to move out.
We both agreed to save the difference we were both saving (we did), but keep the savings separate. The idea was eventually we could use the savings, and sell his flat for a deposit for somewhere together.
Two years after I first moved in with him, we both had savings, I had gained a little inheritance (very unexpectedly), and he had some money left over from the flat sale - we combined all the above and bought a house together (with a mortgage). However, I did say that I would only buy a property with him, if we would eventually get married. 6 months after we moved into our home, we got engaged, and 2 years after that, we married. Now we share all finances etc.
The truth of the matter is, I benefitted massively from moving in with him - I was able to save a lot, but the reality is that he had more equity on his flat, than I had in savings, and the intention was to use that for a house deposit together (at the time, I never expected an inheritance).