So, Georgist land value taxes are a great idea and solve a lot of problems. But it is important to note that they do not solve all problems. That is one of the big hurdles that the idea needs to clear - it is such a good idea that people think it should solve every problem in the world, and then are disappointed when it doesn't. So they declare the idea "bad" because it isn't perfect, rather than accepting that there is no such thing as a perfect solution to all problems.

just because the government decides to spend it’s money on the military

There is nothing preventing the government from doing this right now. Henry George proposed returning the land value tax equally among citizens as a "citizen's dividend", which would solve this problem, but might not be an optimal use of the money. But governments spending money poorly is just a big problem in general.

prevent people from being forced out of their homes

When we build more housing, housing gets cheaper. Certainly it is a tragedy when a family is forced out of their beloved home. But it is also a tragedy when a family cannot find housing at their price point because more housing was never built. The difference is that the first scenario is just more visible than the second. With any change in land use policy, there will be some people who end up getting the short end of the stick. But it is clear that the long term benefits of making better use of existing land outweigh the negative impacts to a subset of the population who is forced from their homes. Unfortunately, policy makers must take a utilitarian view of harms and benefits in order to make sensible policies.

At the same time, there is no reason we couldn't choose some kind if gradual implementation path in order to minimize these negative consequences. The obvious one is to inform all land owners of their potential LVT tax burden, and allow them to choose either to switch to LVT or to stay with their current taxation scheme. Allow them to keep this choice as long as they want, until the land changes ownership - or after a certain time period for corporate land holdings.

relatively ideal density

There is no such thing as "ideal density", because different people want different things, at different price points. Some people want to live in Manhattan, and some people want to live in Montana, and these options should be available to people, even if they dont always get exactly what they want.

If land is very valuable in a neighborhood, then there should be more housing there. Sure, maybe some people would prefer to live in a townhome in that neighborhood. Some people might want a ranch style house on 5 acres in that neighborhood. But if the land is very valuable, this is a good indication that more, denser housing should be built there so that more people can enjoy the value that the area provides. Allowing people to continue living in low-density housing on very valuable land is allowing these people to hoard this value for themselves.

As land value taxes increase the effective rent on this land, the people who live there will have a choice: pay more to continue living in low density housing, choose to live in higher density housing in the same place, or move to a different place with lower density housing. There is no "wrong" choice, but it is a choice these people should have to make, rather than being allowed to hoard valuable land.

our suburbs and in-city suburbs are generally not near transit, and thus not nearly as land valuable and not as well suited for density.

These are mutable facts about the land. Land value taxes solve a lot of problems, but they work best with sensible zoning reform and appropriate infrastructure development. Low density suburbs should be upzoned and served by transit, along with cycling infrastructure. Importantly, these areas should allow a mix of uses to be built anywhere, allowing shops and social centers to be built among the housing, reducing residents need to commute long distances in the first place.

As a final note - in far to many places in north america, we have overbuilt our infrastructure for the sake of providing people with low density housing at any cost. This should stop. Low density areas need to pay their fair share for the infrastructure that serves them - either by downgrading their infrastructure (eg, gravelling roads), increasing taxes, or increasing the density of their communities until they have sufficient residents that the individual tax burdens are reasonable. They should not get to free-ride off of the more productive (not to mention more egalitarian and ecofriendly) parts of their cities.

It seems like we would end up tearing down all our ideal housing and replacing it with over dense housing, rather than building transit out to the less dense areas where it’s needed.

In general, infrastructure should follow development, not lead it. But thats besides the point. Land value taxes have the biggest impact and create the biggest changes in undervalued land. A rowhouse downtown might see a slight tax increase, with some modest pressure to be redeveloped into a small apartment building. But the surface parking lot across the street will see a huge tax increase. The single family homes out in the burbs might even see a decrease in taxes (since their land is mostly worthless), but the "Up House" will see a huge tax increase. The biggest impact of land value taxes is to stop speculation - land owners who hold a piece of valuable land for decades watching the value go up as everyone else makes the area better and better, only to sell and profit by doing nothing but sitting on their ass.

As far as getting the government to intelligently expand their transit infrastructure to encourage more medium density areas.... again - Georgism is not the solution to all problems. I'm not saying this is not a legitimate problem. It just isn't one of the problems that Georgism solves. This problem requires a different solution, like better guidelines for infrastructure development, or more citizen advocacy for improved transit service.