I also think big zap providers should want to host their own zaps (in addition to whatever they were told to publish to) and clients will know that and fetch zaps directly from them.
Discussion
How will clients know that they should load the zap notes from the zap provider?
I thought the idea was that those should be published to those relays that also have the note (the note that was paid)
I don't know, I don't think there is a consensus. If you think that you can publish the zaps to the relays that have the note.
I think that will work in some cases, but not in others. For example, where do you read replies from? You can be following some profile on an open relay full of spam, but you don't care since you're only fetching notes from that person you're following -- but you don't want to fetch replies to that note from that same relay, since they will be all spam replies, you want to fetch replies only from safer relays, paid or with other antispam techniques built in.
Same could apply to zaps -- although zaps already have an antispam mechanism. If zaps had an indexed "m" tag (for "msatoshi") that could allow clients to filter out very small zaps and that would be better.