First let me correct something.
There is a comment above about Agfa introducing color couplers. They did not. They introduced plain couplers which formed colors. Kodak introduced color couplers which formed a mix of 2 color images and masked or corrected color giving better color purity.
Before E6 and C41, all processes were totally proprietary and the films were incompatible from each manufacturer. It was mainly due to the Fischer vs Kodacolor coupler differences, but also a design decision to use CD1, CD2, CD3 etc etc etc.
Now, up until the Concent Decree, film was sold with processing included. You had to return it to the manufacturer or one of its subsidiaries for processing. US courts ruled that was illegal and Kodak was forced for the first time to sell processing chemistry for outside use.
This resulted in a complete redesign of films and processes and the sale for the first time of Type "C" and Type "R" paper in the US. The process redesign was so that non-technical type people could run it safely and under control without special equipment.
For example, one process used CD1, which causes allergies and is not very stable in solution (it forms a tarry oil on the developer solution) and the dyes of that era were not stable enough, so they changed to CD3 which is much less toxic and more soluable.
Another example is that film and paper used a sulfuric acid / quinone bleach bath which was quite corrosive so Kodak changed to ferricyanide which was much less toxic and corrosive.
Processes of that era (50s - early 60s) were at 68 deg F - 76 deg F and took an hour or more. The products were very soft.
As time progressed, the processes heated up and processing time was reduced.
But, Agfa, Gevaert, Konishiroku and Fuji still produced films that were incompatible with each other and these companies still used Fischer couplers due to the Kodak patents on their couplers and their multilayer coating processes. This gave them a huge advantage in coating speed and quality. Finally the patents either expired or the technology was licensed at about the time E6 and C41 and EP3 came on the market in the late 60s - late 70s.
Several of the companies made film compatible with Kodachrome though, but stopped in the 80s. At that time, Fujichrome was a Kodachrome type film but became an E6 type film. In about 1990, Fujichrome film suddenly became incompatible with E6 and almost ruined the company due to this serious fault. No one really knows what happened, but there were several articles in the trade press in the 90s. Now, this is carefully controlled by all companies.
However, Fuji recently announced a new process for the CA papers which require a new developer and blix. These new papers contain Tellurium sensitized emulsions and are, according to Fuji, incompatible with Kodak or Fuji RA developers and blixes.
PE