Property taxes pegged to market value are an incentive for liquidity in the real estate market.
In both cases (SFH on less valuable land, condos on more valuable land) the land shouldn't end up being the majority of the value, since with condos the land value is effectively split among all units in the building.
You can provide land tax subsidies or rebates to targeted individuals (eg the disabled, the retired) without providing massive tax breaks to everyone else.
What's more, this system makes it impossible for, say, retired people to downsize or move because that resets their tax base to a much higher level on their new property (in the Prop 13 case).
I assume there would be limited capacity for abuse just so long as the break only applies to your primary residence.
The tax break wouldn't be so bad if it only applied to primary residence, was means-tested, and couldn't be passed down to children. Regardless, though, homeowners tend to be more well-off than tenants; they shouldn't be receiving tax breaks in the first place.
Prop 13 empowers NIMBYs to vote to kill new construction, strangling supply and pushing prices up, without facing any of the consequences of those rising prices.
Your proposal would force this woman from her home as her land value tax rose (As she has no ability to pay for this increasing tax burden)