Why is this phrased as if it's Cloudflare's fault? If it's this easy for a side effect of a recapcha image to de-anonymize a Tor user, then this seems like a failing of the Tor protocol that they should fix. Maybe they need to introduce more jitter, repackage requests into a single stream with consistent (or randomized) packet size, or pad the packets with random data.
Introducing jitter would mean increasing latency and generally slowing down your browsing.
I mean, using a VPN is slower than not, but tons of people use them