The housing capacity of neighborhoods can be greatly increased w/o destroying their character. Seattle is now permitting additional dwelling units, e.g. "mother-in-law"s and tiny houses, on existing properties and I can assure you that they are being built. The rents on them are well below what a developer of the density buildings, (which steal the views and charm of existing homes and transfer that value to developers and to realtors like Redfin), would charge.
LVT is a good idea. If it convinces neighborhoods to accept re-zoning then fine. If not then just use the tax dollars to promote housing. One good use would be improving transit to help neighborhoods handle more residents and to reduce the need for cars. Fewer cars could mean fewer garages, which in turn could become more auxiliary dwelling units.