Counterpoints:

• TOML is intended for configuration, not for data serialization, so you shouldn't be sending it over the wire in all too crazy ways anyways.
• Most protocols will have a built-in way of knowing when the whole content has been transferred, typically by putting a content length into the header.
• Having to wait until the closing } or ] can also be a disadvantage of JSON, since you cannot stream it, i.e. start processing the fields/elements before the whole thing has arrived. (You probably still don't want to use TOML for that, though. JSONL, CSV or such are a better idea.)