Moving Git past SHA-1

There are two reasons to not simply extend the SHA-1 construction:

1. The "heat death of the universe" depends on an attacker having to perform all the operations we expect them to. A break (such as the current break for SHA-1) allows an attacker to get the result they need without doing all the operations we expect them to. Thus, we get a shorter hash by using a new, unbroken construction like SHA-2 or SHA-3, rather than by extending SHA-1 out far enough that even with the attacker's ability to skip operations, they can't feasibly compute colliding hashes under any circumstances.
2. Once one break is found, it's likely that someone will build on this work to reduce the difficulty of the break. Thus, if you extend the broken construction, someone is quite likely to find a way to simply not bother with the extended bit.

That second point is a doozy - you expect 2⁸⁰ operations (as it's 160 bits long - a 256 bit hash would need 2¹²⁸ operations) to break SHA-1, but the attack reduces that to around 2⁶³ operations. You may be able to extend it to 2⁸⁰ operations by extending the hash to (say) 200 bits, but an attacker building on the recent work could then reduce it back down to 2⁶³ operations, and you've got to pay the cost of a new hash again.