Your theory makes sense until it falls apart if you consider SE and Mini as the same category of small iPhones. If the only reason why Mini failed was bad launch time, then why haven't Apple launched anything small (SE or Mini) after 2022? Isn't 2024 or even 2025 the perfect time to launch an upgrade for SE or Mini? They now have enough data since the last launch of a small phone.
The problem is that people who want a small phone prioritize the size.
Most of them don't care about the premium features of larger phones. So the Mini was a weird niche within a niche. Small phone with premium price and features.
The Mini and SE2 were virtually identical in physical size. For the 16e they should have used the iPhone 12/13 Mini body and the 13 Mini screen. Use the 15 Pro SoC with 8GB memory, and the 15 camera. Sell it for an SE price. Now you have fused the small phone and budget iPhone markets.
I can confirm, that Apple my misunderstood the market:
I was eager to buy a new iPhone because I just finished my masters degree and started a new job, had a bit of money and than the SE2 launched. My 5s or SE1 started to age and as an beginner app developer a current phone was important. I was so happy because I could not see my self using one of those bigger phones even though the SE2 was still bigger than my 5s/SE1. A few months later the mini was released and my initial reaction was "OMG this is THE perfect phone, but I just got a new one... i can not afford to buy another one".
iPhone SE 1st gen 2016 (Discontinued 2018)
iPhone 12 Mini 2020 (Discontinued 2022)
iPhone SE 2nd gen 2020 (Discontinued 2022)
iPhone 13 Mini 2021 (Discontinued 2023)
iPhone SE 3rd gen 2022 (Discontinued 2025)