Tests provide certain guarantees where compiler proofs (e.g. compile-time errors) are absent. You don't need a large project to realize those guarantees.
Tests aren't just for initial correctness---their benefit is largely in maintenance. They allow you to make changes or refactor the system with guarantees that the covered portions still operate as they were originally designed. There is really no excuse for those types of breaks.
Then there's the team setting: I'm not the only one writing my code. Someone else has to get in there and make changes. I might have to come back months or years later and make changes. At work, we have five developers touching over 100 distinct projects at any point. We have observed that the lack of tests essentially guarantees breaks---we have QA, and there is a direct correlation between bugs and whether code is comprehensively tested.
With regards to TDD: we also observe time and time again that writing code after tests yields untested behavior. There are always odd cases that might not be immediately obvious. There might be a bug that was inadvertently introduced, and now that bug is tested as part of the implementation. Certain branches may not be fully tested. I've seen comments here about this being an experience thing---that more senior developers won't have this problem. That's essentially saying that one is infallible; it doesn't make sense.
TDD also prohibits rushing. Not writing tests is also an excuse to rush the implementation and produce a shitton of unnecessary code. Tests slow you down and force you to think.
Small projects grow. If you don't write tests upfront, when do you write them? We develop incrementally---all of our projects start small, and some of them will remain small for perhaps a year or more until we revisit it. Writing tests at that point loses a lot: we may have forgotten the details of the implementation by then, and the person who originally wrote it might not be involved at all in the changes.
Tests aren't just for initial correctness---their benefit is largely in maintenance. They allow you to make changes or refactor the system with guarantees that the covered portions still operate as they were originally designed. There is really no excuse for those types of breaks.
Then there's the team setting: I'm not the only one writing my code. Someone else has to get in there and make changes. I might have to come back months or years later and make changes. At work, we have five developers touching over 100 distinct projects at any point. We have observed that the lack of tests essentially guarantees breaks---we have QA, and there is a direct correlation between bugs and whether code is comprehensively tested.
With regards to TDD: we also observe time and time again that writing code after tests yields untested behavior. There are always odd cases that might not be immediately obvious. There might be a bug that was inadvertently introduced, and now that bug is tested as part of the implementation. Certain branches may not be fully tested. I've seen comments here about this being an experience thing---that more senior developers won't have this problem. That's essentially saying that one is infallible; it doesn't make sense.
TDD also prohibits rushing. Not writing tests is also an excuse to rush the implementation and produce a shitton of unnecessary code. Tests slow you down and force you to think.
Small projects grow. If you don't write tests upfront, when do you write them? We develop incrementally---all of our projects start small, and some of them will remain small for perhaps a year or more until we revisit it. Writing tests at that point loses a lot: we may have forgotten the details of the implementation by then, and the person who originally wrote it might not be involved at all in the changes.