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I think understand the advantages of using a vector clock instead of a timestamp and the advantages of a bloom clock vs vector clocks.

But since a bloom clock can sometimes return an incorrect order of events (false positives), wouldn't using the timestamp be a simpler solution on most cases that can allow some unordered events?

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Author of the paper here. Imagine it like this, if your bloom filter overlaps by a lot an incoming bloom filter, what you can do is go over your logs, find the bloom filter closest by increments to the incoming bloom filter, and then compare them. If the events are not comparable, i.e. concurrent, you will know it immediately. If they are comparable, your false positive rate now will be extremely low (because you picked the bloom filter in your logs that is closest to the one you received).

It's important to keep in mind that the reason we use vector clocks in the first place is because timestamps also can return the incorrect order of events because of time drift, delivery times, etc.

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