1. Nobody is making that assumption. I already described two ways non-housing expenses go up with real estate. There are many more.
2. Cities need to build schools, water pipes, roads, traffic signals, etc when new people move to the area. Many of these expenses are immediate and impact fees aren't going to be high enough.
Tax caps are counter productive and there are no shortage of problems with funding fundamental services through municipal budgets. But taxing real estate can make sense.
Property tax caps also incentivize people to not move, which in a city like LA contributes to our traffic issue. If I live in Beverly Grove for 15 years, and my house has appreciated from $350k to $1.2M, and my new job has relocated from Century City to Pasadena (about a 20 mile difference), I may not be willing to move as my property taxes would jump substantially. Now, you're just adding another car occupying the freeway for an hour each way during rush hour.
Tax caps are the lesser evil. Without them, time and time again, city management has shown irresponsibility.
The proposed modification, to a per-person cap, solves your complaint about new people moving to the area. If the cap is $4,000 per person and there are 40,000 people, the budget is $160,000,000. If another 10,000 people show up, for a total of 50,000, then the budget rises to $200,000,000. Each landowner pays their portion of the resulting budget according to land value.
2. Cities need to build schools, water pipes, roads, traffic signals, etc when new people move to the area. Many of these expenses are immediate and impact fees aren't going to be high enough.
Tax caps are counter productive and there are no shortage of problems with funding fundamental services through municipal budgets. But taxing real estate can make sense.