Exempting by use, like primary homes or day cares, now means that the government is in the business of snooping on you to make sure that the primary home you declare is also your actual primary home. You also give well-off people with a bigger primary home (or owning a home at all instead of renting) a big tax break. Welfare for the well-off is not an efficient use of funds.
> - Do you introduce alternative tax sources (i.e. increase income taxes on billionaires instead as in California)?
If you do that, you lower your land value tax take. (Of course, if you already already sabotaged your land value tax base via exemption and limits, as per your second point, then bad decisions beget more bad decisions and special taxes on billionaires seem like a good idea..)