I like to cage my tomatoes...keeping them off the ground helps them ripen better with less rot, and they are easier to pick. But I used to let them sprawl, back when I put out 100 every year. It's sure a lot less trouble, and if you straw them well, you won't have any problems (except your back, from picking them).
I straw mine anyway...in fact, I use 4-6" straw on my whole garden, once it gets going good. It keeps the moisture in and the weeds out, then rots over the winter, gets tilled in, and improves the soil every year.
Another hint on growing tomatoes...don't overfeed them, or you will get all vine and few tomatoes. They do make special tomato food, but I just give them one or two shots of Miracle Grow when they are getting started, then leave them alone except for watering. A tomato is 90% water, so it's essential that they get plenty of H2O.
One shot of feed is enough for peppers, just to get them out of the shock from being in those little containters. They thrive on heat and poor soil, and the hot and banana peppers will withstand a lot of drought. But the big sweet red, golden and yellow ones that I love need a fair amount of water.
I hope this helps you all with your gardens!