If I do a search on jisho.org for おきます, I get matches for 起きる and 熾きる through deinflection, but not 置く, even though 置きます does. Is this because 起きる and 熾きる have pronunciations of おきる whereas 置く has a pronunciation of おく, and jisho.org fails to try "おく" after trying "おきる"?
If you search for
おきます, jisho.org gives you a little popup saying
おきます could be an inflection of おきる, with these forms: Masu-form. It is the polite form of the verb.
My guess is that the answer to your question is something along the lines of "because the code for unconjugating search terms produces only one suggestion, and tries ichidan verbs first". Basically, I think you're right on the mark.
That said, the only people who can really give you an answer as to why
置く is not a result of searches for
おきます are going to be the jisho.org authors, because this is a function of they way they've built their site. You can find their contact info on jisho.org's "about" page.
I suspect it is an issue with how jisho.org searches for inflected words, as you suggested. Online Japanese dictionaries usually provide all possible variations of a search term which is an inflected word. For example, Weblio gives 置く in its suggestions for おきます.
Furthermore, if you search for かえります on jisho.org, it says "Searched for かえる. No matches for かえります". Then it shows the correct 帰る first but also suggests 変える and 換える, which do not conjugate as かえります. That could be potentially confusing for beginners, I imagine. It might be worth contacting them to make them aware of the issue. If you get any further with this, please comment on this thread with any updates :)