Ever since I had to give up eggs, cooking latkes became a nightmare. Thankfully, that is no longer the case. I don’t have a source for this technique, but I did learn about it online somewhere. To the person who thought this up: Thank you!
Grate your potatoes as you normally would, but set one aside. Peel, boil, and mash that last potato, adding it in to the bowl of shredded potatoes and onion. Mix it all together and fry them up as you would any other latke. No eggs needed!
I have not yet tried this with sweet potatoes, but will try to update the post with my results.