Bold doesn't make you more convincing nor right - never does.
I think the problem here is that "successor" means whatever the person arguing wants it to mean.
The other problem is that the i3/i5/i7 denomination is
branding not
specification and represents price-point and intended market segment, not absolute performance. Its also a highly unsatisfactory, dumbed-down system that totally fails to communicate the half-dozen or so variables that determine the processor's performance - like most modern marketing, a cynic might think that it was deliberately designed to make it hard for customers to objectively compare products.
So, in terms of
intended market position and price point the "successor" to the i5-7400 is the i5-8400
because that's why Intel stuck that label on. In terms of absolute performance - well, looks like the i3-8100 might even
be an i5-7400 (in an industry where the only difference between a 3GHz part and a 4GHz part may well be that the latter has been tested at the higher frequency).
Really, i3/i5/i7 is no different to "standard/premium/pro" - and the complaint is that, with the 8th generation processors, Intel started offering 6 cores instead of 4 at the "premium" price point but, instead of passing that improvement on, Apple decided to downgrade from a "premium" to a "standard" processor and pocket the savings. This is technology, not the price of a loaf or bread. Technology advances, and after two years it is entirely reasonable to expect significantly better specs - such as more/faster cores - for the same price.
than there's no logically reason not to apply that to the Mac Mini upgrade.
Yes there is and its already been explained to you. Its never been valid to use i-number branding to compare low-power mobile and desktop chips. The iMac could have had the i5-8400 as a straightforward (maybe even drop-in) replacement for the i5-7400. The innards of the new Mac Mini have been changed beyond recognition to accommodate desktop-class processors - different socket, different power, different cooling.
Still, It is entirely arguable that - in branding/price point terms - that even the entry-level New Mac Mini is
not a cheap computer and it should come with a "premium" (relative to today's range) i5 processor, not an i3.
Its equally true that the new entry-level i3 Mini
substantially out-performs the
top-end 2014 model - but that's because (a) its a 65W desktop processor vs. a 25W mobile processor and (b) 4 years have passed and processors have more, and faster, cores for the same price.
By your argument, Apple should have put a 2-core Celeron or similar in the new mini, as that would quite likely be just a little bit better than a 4-year-old i5. I don't think that would have gone down very well unless they had also slashed the price.