That's not necessarily a good solution either, because a service could figure out that the source of random fingerprint data likely comes from the same user. Especially if your ip is not changing. It might perhaps be effective if a substantial amount of people were doing it though.
But to generate such random fingerprint is difficult because it consists of many parts and services don't all build fingerprints the aame way. You could easily randomize e.g. canvas data, but the issue is that if you only randomize one data point then that one random data point pretty uniquely identifies you if your other datapoints are stable. So to be effective you would really need to randomize several different datapoints and that may not be such an easy task since websites could build them in all sorts of ways.