Far as I know, could gain L4 without teaching. Provided you are a good enough skier and knowledgable enough for the teaching. At least it was that way up to three years ago. This is unlike some other national associations where it is necessary to have obtained a certain number of hours of paid instructing experience to progress to the next level.
L1 and L2 are not that difficult to pass and can be done by a reasonably competent skier attending the appropriate CSIA L1/L2 workshops. At L1/L2 ski and teach are all assessed at the same time. (At least when I did them.)
L3 is a big step up. The skiing and the teach are separate exams. The CSIA workshops will help in understanding the level of proficiency required for both the ski and teach but, as I understand it, candidates are expected to undertake development over and above those workshops to have a good chance of meeting the standard. Ski schools may provide some of this development or there's the opportunity to pick up a mentor and/or ski with others on the same path. If not working as an instructor there are various organisations that offer multi-week (typically 6-8 week) programs for L3. There are other groups that provide shorter programs e.g. 5 days and may need to do more than one of those.
MHO don't need to be a bump pro to pass L3 ski assessment. I passed the ski-off aged 64 y/o - not yet passed the teach. There's some youtube vids around that show the standard required for each of the L3 ski tasks (IP, AP, Shorts, bumps). May have to dig around in the archive to find those. One series of vids shows skiers doing the tasks and describes where they meet or fall short of the standard. The other series shows skiers doing their runs and then shows scores. A 6 or above is needed to pass ski cert. IP and bumps must be passed and the average score must also be 6 or above. Candidates get two runs at each task and best score is selected.
More recently they have added an extra ski task to be decided on the day - either braquage or hop turns - and there are vid demos of those as well.
AFAIK there are no similar vids for the L3 teaching - probably too 'student' and situation dependent.
MHO doing instructor certs is a good way to develop as a skier and quite cost effective compared to ski school lessons. Have also done a multi-week development program. Big $$'s but it was a necessary stepping stone (for me). I still do the CSIA Adv Ski and Teach workshops once or twice a season when they are available.