Your premise doesn’t make sense. A land value tax would not “increase all of their costs at the same time”, unless the tax was implemented in such a way. More realistic would be that the tax would be revenue neutral, such that taxes would increase per unit dwelling on land with poor utilization, but decrease on land with better utilization (i.e denser). This would be reflected in rents and would encourage people to move to denser neighborhoods because the rents would be cheaper.