> Communicating with legislators isn't what's considered lobbying

It basically is.

You may be thinking of who is considered a lobbyist or lobbying firm, which is (roughly, different laws on the matter have different specific definitions) someone (or some firm) who (or which) is paid to lobby on behalf of one or more other persons or entities.

> How would it be ineffective?

Because even if you are able to police it effectively, then the people that have money will instead lobby personally rather than hiring lobbyists, while hiring staff to do all the legislative drafting and organizational support work for their personal lobbying (but not actually doing the lobbying itself) as well as continuing to use the unlimited campaign financing channels opened by Buckley v. Valeo and Citizens United to get people who they don't need to lobby once in office to convince them to vote in line with their interests elected.