Why can't I find allium-free main and side dishes on your site?

I can't eat them either, so I leave them out.

I'm in the same boat. I've been adapting recipes for years. Omitting the allium family from some recipes is simply not going to create something good: they require substitutes for both the bulk & texture they would add to a dish. I've used finely chopped celery, or fennel bulb in many dishes, esp veg patties...
a fab cookbook that seems to be out of print right now is "Best of Lord Krishna's Cuisine" by Yamuna Devi. (I use less than half the hot peppers & omit the asafetida/hing tho). No onions, no garlic, no 'srooms for her all-vegetarian recipes. I've made some excellent food from this book.
https://www.amazon.ca/Best-Lord-Krishnas-Cuisine-Vegetarian/dp/0452266831
or the original book: https://www.amazon.ca/Lord-Krishnas-Cuisine-Vegetarian-Cooking/dp/0525245642

As someone who is on restricted diet (low-FODMAP, which includes no garlic/onion among other things), I totally get your frustration. Food52 is a great site for so many things, but it's not super helpful for folks with special dietary needs. The new "special considerations" filter on search goes a long way, but not far enough for a lot of us. Maybe it would be possible in the future to add a feature where folks could tag their dishes as appropriate for special diets. While I wait for that to happen (not holding my breath), I'll continue to do as I've done -- seek out recipes that seem yummy and make accommodations. BTW, the cookbook that is my go-to and includes all allium-free (and low-FODMAP) recipes is The Quiet Gut by Sonoma Press. It is a horrible title for a book, but the recipes just work. Kate Scarlata's blog is also a great resource for allium-free recipes. (Links for both below)

https://www.amazon.com/Quiet-Gut-Cookbook-Low-FODMAP-Symptoms/dp/1942411014
http://blog.katescarlata.com/category/recipes/

I'm not a fan of alliums - so I just leave them out when a recipe calls for them. No one I cook with misses them, either! There's almost nothing you can't make by just leaving them out. (Except of course something like onion soup, or garlic whatever, but those wouldn't be anywhere near my menu anyway!)

If there are enough allium averse cooks out there to make it worth categorizing and seeking recipes, this is probably as good a place as they'll get to make it known. My mother wouldn't be in the same room with an onion, but pretty much had to find her own way; fortunately, that suited her well. I, on the other hand, am apt to be cutting up an onion while I'm still deciding what to make. This site doesn't seem to be much for polls, but the powers that be do monitor these questions and would doubtless be glad to hear from people who would be interested in something like that.

In many cases, when I type in "no onion," "no garlic," or "no allium," the sites respond with recipes full of those ingredients! The few that I've found that don't post those forbidden-to-me ingredients have limited recipes. I was truly hoping this site would be more interesting and helpful.

Have you tried doing a general Google search of "no onion and garlic recipes" There are already out there or you simply omit those ingredients and amp up the spices or other ingredients to keep the flavor.