Would SHA1 be broken by sheer brute force, even if it had no weaknesses of its own? It is well-known that SHA1 is broken.  Collisions have already been achieved.

Current algorithms for finding collisions leave a “fingerprint” in the collision files, which can easily be detected.  It is claimed that brute-force would not be practical, since that would require $2^{80}$ time.

However, I am not so sure if $2^{80}$ time is that impractical.  My understanding is that the Bitcoin mining network together generates about $7*2^{89}$ hashes per year.  That is enough to break any system with 80 bits of security by sheer brute force.  I know that it uses dedicated hardware that cannot be repurposed.  But creating such hardware would be well within the capabilities of a nation state.  And cryptosystems are supposed to be secure against such adversaries.  Furthermore, there are other cryptosystems with 80 bits of security, and some are still being proposed today (!)

Just how feasable is this attack?
Yes, it is now conceivable to find a SHA-1 collision by brute force.

The general method is outlined in Paul C. van Oorschot and Michael J. Wiener's Parallel Collision Search with Cryptanalytic Applications (in Journal of Cryptology, 1999; free earlier version available from the first author's website; expands on an article presented at CACM 1994). It uses local search iterating hashing; when a distinguished value (say with a certain number of zeroes in low-order bits) is found, it is reported to a central location; enough findings lead to a collision. It is expected that less than $2^{82}$ hashes (and comparatively little extra work) are required to find a collision.

By May 2018, the bitcoin mining aggregate hash rate is reportedly $30\cdot10^{18}$ SHA-256d per second ($2^{81.1}$ per day), where SHA-256d uses two SHA-256, and SHA-256 is roughly as costly as SHA-1. The ASICs predominantly used for that can not be directly repurposed for a SHA-1 collision search: they use SHA-256d, not SHA-1; and as an aside they hash incremental values, rather than iterated ones. However the technology is there.

Thus the energy spent in a day of bitcoin mining is enough to find a SHA-1 collision by brute force, hypothesizing the same technology is used. The collision found would be a random one, with chosen prefix decided at start of attack, and could not be detected.

And it might well be that significantly less work would be enough to find a collision that evades detection using the current "fingerprint" method, by using specially crafted (but less efficient) differentials than used to find the first collision reported.