This was part of the official reasoning. In practice, the tax was designed to be enough of a burden to incentivize conversion.

So were all the restrictions placed upon them: they couldn’t carry weapons, they couldn’t ride horses or camels, they couldn’t build new houses of worship, they couldn’t testify against Muslims in criminal cases, their houses couldn’t overlook Muslim ones, they couldn’t practice their religion in certain ways (no public religious processions, no ringing church bells or blowing the shofar, etc.)…the only way to stop being a second-class citizen was converting to Islam.