Can we stop recommending fontspec as first choice in case lualatex is used?

fontspec doesn't change the math setup to unicode math fonts -- this is done by unicode-math -- it only change some math alphabet like \mathrm and with the option no-math you could avoid this too. So if you have a good (sans-serif)math setup that works with pdflatex or with lualatex and luainputenc you can use it with lualatex and fontspec too.

Beside this you seem to have a quite "english writer" view and don't bother about other scripts. I believe you that you choose luatex because of the lua scripts. But most people switch to xelatex or lualatex to be able to use system fonts and to easily write in non-latin scripts -- you only need to look at lualatex related questions to see this.

One reason to rely on fontspec over luainputenc comes from the package documentation of the second package. The abstract says simply:

Input encoding management for LuaTeX, needed only for compatibility with old documents. For new documents, using UTF-8 encoding and Unicode fonts is strongly recommended. You’ve been warned!

Then, the first section of the document, entitled "Overview: When (not) to use this package" reads:

This package is strictly meant for compatibility. It is usefull [sic] in the two (overlapping) following cases:

1. Your source is not encoded in UTF-8 and you don’t want to reencode it for some reason.
2. Your document is using legacy 8-bit fonts (with fontenc), as opposed to modern Unicode fonts (most probably with fontspec or luaotfload and fontenc with option EU2).

The same section then continues (in part):

luainputenc has several modes of operation. By default, it basically turns LuaTEX into an 8-bit engine, which means you loose half of the benefits from using LuaTEX.

In any event, I think it is fairly clear that, as the author of the package himself does not recommend using luainputenc for "new" documents, there is little reason for others to recommend it to other users. It does not seem to be recommended for the purpose you are using the package. (Which is perhaps fine: you have taken the time to explore what best suits your needs.)

Of course, one may choose to use this package over fontspec (I wish LuaTeX-based documents compiled more quickly, too!), but it seems a stretch to say that fontspec (or luaotfload) should not be recommended---especially to new users---before luainputenc. I am certainly not inclined to do so.