Elon has said on numerous occasions that other companies are welcome to share the supercharger network, but their cars need to pay for their share (whether the owners or the company pays for it he doesn't care).
There are rumors Tesla has been working on a combined CHaDEMO/CCS adapter and Tesla did join the group that controls the CCS standard.
I do want to see if they actually achieve the 350KW goal in the real world. So far very few CCS stations are anywhere near the theoretical maximum power. Tesla has been finding that when superchargers get a lot of use, as they do in California, they wear out quickly and 350KW chargers are going to have even worse heat problems than Tesla does. There are some engineering challenges to long term reliability of these stations.
Basically the higher the power of the station, the more heat there is to deal with. Copper has one of the smallest resistivities of any material (which is why it's used so much for conductors), but it's resistivity is not zero and there are I^2R losses. 350KW going through the system is going to generate a lot of heat, even more than the superchargers. The more the system is used, the less chance it gets to cool down between use and everything starts to degrade from heat damage.
I also hope the cars built to handle these chargers will be able to deal with the battery heating on board as they batteries are quick charged at such high currents. The approach Tesla uses for batteries is different than the rest of the industry. The rest of the industry uses fewer, larger batteries and Tesla uses a lot of small batteries. With a lot of smaller cells, the actual current going into each individual cell when supercharging is not huge. It's enough the car needs to switch the cooling system to maximum, but each cell is only getting about 0.25A. But with larger cells, each cell could be getting much more current when charging.
Each cell can be surrounded with a cooling system, but the cooling system can't be inside. By using smaller cells, Tesla can cool the individual cells more efficiently. The reason they have said that the optimum cell size is the 21700 that will be built at the GigaFactory has a lot to do with efficient cooling when charging. Car makers with large cell batteries may find they can't keep them cool enough when fast charging at the rates advertised.
The heating is also another problem, it's a net loss of energy. Slow speed charging gets more energy from the grid into the car, the faster the charger, the more energy is lost from heat.
I recently saw a lecture on YouTube that was given by one of the founders of Tesla. He left just before the Model S was introduced and now works as an industry consultant. This was a couple of years old, but he said working with car makers, they don't have the basic talent to make EVs. They have farmed out so much of the car that the only expertise they still had was making ICE motors and final assembly. Few electrical engineers were employed by car companies at the time of his lecture. That may have changed a little, but the much touted Chevy Bolt is largely an LG design put into a modified GM car platform.
The car companies may come through on this eventually, but they are about 5 years behind Tesla on lessons learned on everything involved in making long range EVs. They also have a lot of internal resistance from hide-bound executives who are resistant to give up the massive investment these companies have made in engine tech.
