At one of my first jobs as a student employee they offered me a salary X. In the contract there was some lower number Y. When I pointed this out, they said "X includes the bonus. It's not in the contract but we've never not paid it". OK, if this is really guaranteed, you can make that the salary and put it in writing. They did, my salary was X and that year was the first time they didn't pay the optional bonus. Didn't affect me, because I had my salary X.

IANAL and I don't know how binding this is. I'd think it's crucial for it to be in both copies of the contract, otherwise you could have just crossed it out after the fact, which would of course not be legally binding at all and probably fraud (?)

In practice, it doesn't really come up, because the legal department will produce a modified contract or start negotiating the point. The key is that the ball is now in their court. You've done your part, are ready and rearin' to go, and they are the ones holding things up and being difficult, for something that according to them isn't important.

UPDATE:

I think it's important to note that I am also perfectly fine with a verbal agreement.

A working relationship depends on mutual trust, so a contract is there for putting in a drawer and never looking at it again...and conversely if you are looking at it again after signing, both the trust and the working relationship are most likely over.

But it has to be consistent: if you insist on a binding written agreement, then I will make sure what is written is acceptable to me. You don't get to pick and choose.

However it can be disputed, and a company could argue about the timing or details.

That’s why you’re often asked to initial changes, makes it clear that both parties have agreed to the modifications.