I've never carried a spare mask...but a few months ago, the band on my mask broke...so i spent the rest of the dive holding the mask in place with 1 hand...very big PITA!!!!!!
I once whacked my mask and broke the buckle while hauling out all the parts of the dive platform I was going to set up for a coming class. I then did the entire setup dive without a strap, but without holding the mask on. I only had to touch it to make an adjustment a few times. If you have inhaled slightly to create a suction and are not subsequently exhaling through your nose, it should stay on just fine without the strap. Practice keeping the mask in place without a strap in the comfort of your home for a while, then try it under water. You'll be surprised how easy it can be.
Like many others, my decision about carrying a mask depends upon the situation. In all dives and with all accessory equipment, you have to weigh the likelihood of a problem against the consequences of it occurring and the inconvenience of carrying it. When I am cave diving, I carry 3 lights. The likelihood of needing 3 lights is small, but the consequence of needing that 3rd light is dire, and it is no big deal to carry it.
Similarly, the likelihood of a mask failure is extremely remote, and for OW dives the consequences are minor and the inconvenience of carrying it higher (it's bulky in a suit pocket,. and I don't use a BCD with pockets), so I will not carry one then.
In caves it is a different story, but I know some extremely veteran cave divers, some with names that are huge in that history, who do not carry spare masks in caves. One of them said to me, "I have been diving caves for 35 years and haven't seen a lost mask yet." Another says he wants to be as streamlined as possible in a cave, and so he doesn't want that bulk in a pocket. In the extremely unlikely situation that a mask would fail, he would just get on the line and follow it out.
I will confess that I have done cave dives without one myself--especially if I know my buddy has one.