I would not exactly call NES font editing that simple, indeed the NES lacking power in some cases means it had to do things that I would hate to have to handle in the consoles I tend to deal in.
Anyway the PS1's 2d was mostly just a 3d texture, though it was known and handled much like 2d traditionally is/was. Some games did do text as an actual picture, quite possibly including some bigger games. You can search through looking for choice file names, directory names, elimination of other files (if it is clearly 3d models it is not going to be the font...), file sizes and more. You can scan through with a viewer but the PS1 did have some higher level formats which make that harder, to say nothing of the options for compression. After this you are probably going to want to look at tracing or the lesser cousin in memory dumping and search -- find the font in the PS1's memory, hope it has not changed between there and the iso and search for fragments from it).
Not sure what the current debugger of choice is for the PS1 but http://problemkaputt.de/psx.htm
would make a decent jumping off point.