The MacBook Air can be used in "clamshell mode" with the lid closed, hidden behind an external monitor and connected to a keyboard and mouse. I'm not saying this is an ideal solution - and it certainly doesn't excuse the lack of a reasonably priced Mini - but you can basically treat it just like a desktop if desired. It has two USB 3.0 ports, thunderbolt port, a headphone jack and an SD card slot on the 13" model. I mostly use my own 2013 11" MacBook Air like this these days.
I think this is what
@EightyTwenty was suggesting.
Despite the MBA only being a generation ahead of the Mini the Broadwell CPU is actually more efficient per clock due to the process shrink (14NM vs 22NM) and the CPUs are very close in benchmarks despite the disparity in clock speed (1.8GHz vs 2.6GHz for the middle model for example) - I would say that only the fact that the MBA has a 15w CPU and therefore probably unable to sustain turbo speeds as long as the Mini edges the Mini out past it.
Ironically, checking up the comparative specs, the HD6000 GPU appears to be more powerful (or comparable) to the Iris Graphics 5100 in the Mini.
This means little for the Mini per se but could be interesting if Apple were indeed looking to bring a Retina Screen to the MBA. Pricing becomes something of a factor when you consider in the UK that a Mac Mini middle SKU upgraded to 256Gb SSD (8Gb as standard) comes to £859 while the upper SKU MBA which can be bought off the shelf with 8Gb RAM and 256Gb SSD costs £1099.
For your extra £240 you get:
A screen (albeit TN non-retina)
A keyboard that isn't compromised
Nice big trackpad
Portable
Don't forget that being an off the shelf model the £1099 MBA is subject to retailer discounts - I have seen it for as little as £949 on the high street whereas an upgraded Mini could only be bought customised at Apple for full price.
Logically, therefore, a generously specified Mac Mini starts to look poor value up against the MBA which has the added value proposition of being a laptop.
If Apple were to give the MBA another speed bump to modern processors - for example giving it a i5-8250u, Thunderbolt 3, and even a retina screen - a Mini starts to look incredibly poor value if the MBA pricing is keen.
The notion of giving the MBA a Retina screen when there's no modern Iris Graphics enabled GPU currently on offer in the 15w range from Intel starts to look feasible for a non-Iris Graphics GPU when you consider that Apple equipped the 2013 and 2014 models with Haswell powered Iris Graphics 5100 which are theoretically outclassed by UHD620 graphics in the modern Coffee Lake U series CPUs. These would be cheaper than the Iris Graphics equipped 28w models so we could see Apple quietly dropping the non touch bar MacBook Pros in exchange for modernising the MBA instead.
Would they keep the Thunderbolt 2 chipset though or give it a more serious upgrade to Thunderbolt 3 while using the 'old' keyboard? Thunderbolt 3 could make the MBA very popular as it would open the door to eGPU support.