However people in this thread, and EV fans in general, seem to make the same mistake when they say "every one has electricity". Upon closer inspection though, that statement is about as relevant as the "hydrogen is the most common element in the universe" for two reasons.
Is there something missing from my analysis?
#1 You are committing the fallacy of false equivalency. The statement "Hydrogen is the most common element in the universe" is not equivalent to "everyone has electricity". The former is irrelevant because, as you know, despite it being a "common element," it doesn't exist purely in nature. The "everyone has electricity" is relevant since it means the necessary backbone infrastructure for plug-ins is already there (we have means to produce and deliver electricity already, enough to power 80% of our current fleet; you can't say the same of hydrogen). An equivalent statement would be "everyone has hydrogen" or to put it more specifically "everyone already has a hydrogen pipe to their house and uses it regularly" or "every gas station already has hydrogen delivery and uses it regularly".
#2 Another fallacy you committed is comparing one time costs (station costs) to ongoing costs (of producing hydrogen). No one is arguing producing electricity is free (something implied by that "common element" argument). Installing a "charging station" is a one time cost. It's the same fallacy people make when comparing lithium with gasoline (which is even more wrong since lithium can be recycled).
#3 is as people mentioned, the current multi-thousand dollar cost of a "charging station" is completely unnecessary and a rip-off, when in reality you can spend about 100 dollars or even $0 to have your own 240V charging socket. Some people can even make do with 120V if their trips are short enough. Also keep in mind the $2500 includes installation costs. You can get one for $700 from GM if you install it yourself. There are plenty of much cheaper options coming from third parties (including ones that you just plug into a socket to "install," saving even installation costs).
#4 Although the public charging stations are primarily publicly funded, the large majority of private/home charging stations will be privately funded and it is actually viable for it to be privately funded, since the unit cost is still relatively low (if you are buying a $30k+ car, you can afford a $1000 charging station). This includes other "public" stations that are funded by private businesses (plenty of those already in California).
All hydrogen stations will be partially or fully publicly funded. No private company wants to do it themselves (even the SunHydro company that said they would do it themselves did it with public funding) because of the high costs, no hydrogen cars for sale, and the fuel costs more than gasoline even when you count higher efficiency of hydrogen cars. That means a decision to go hydrogen has to be mainly supported by tax payers. You can't go part way either and have a working solution, since unlike plug-ins you can't install a station yourself. And despite all the claims of it solving the "range anxiety" problem of EVs, it actually doesn't until you have an infrastructure similar to the current gasoline infrastructure. A PHEV actually is the one that addresses the issue.
With hydrogen you not only have the station cost ( when one costs $3-4million; just to match gasoline infrastructure you need to have 120k stations, or $360-480 billion), but also backbone infrastructure costs (the production/delivery infrastructure).
In summary:
+ hydrogen cars don't emit local emissions (besides from water) and tends to be more efficient than typical ICE
+/- it can be used for long trips, but you need the full infrastructure first
- hydrogen cars will cost more than BEVs, PHEVs, and ICE cars.
- it will cost more to fuel than BEVs, PHEVs, and even ICE cars.
- it completely doesn't work even for daily driving until someone installs a multi-million $ station near you (no one wants to drive 50 miles just to fuel up). Good luck waiting for that to happen.
- uses 2-3x the energy of a plug-in when used with renewable sources (or any other electrolysis sourced hydrogen)