Do academics look down on well-designed academic websites?
As has been stated several times, there is no such thing as a site being "too well designed." Of course the design should take into account the audience that will be viewing the site—i.e. if you are designing a website gallery for minimalist paintings, it would be very odd indeed to use as many buttons and links as Amazon.com, whereas for an online store that isn't a bad design at all.
However, in my view, the keynote is really not so much design as implementation.
There are two crucial factors: file size (also known as website obesity), and overuse of scripts (which is closely related).
The website you linked in the comments doesn't load at all in my browser, because I have scripts disabled by default. I enable them for sites that I expect to run scripts, such as gmail or youtube.
I grant that I may be in a minority of the general web browsing population...but I expect a disproportionate number of academics are aware of such things, and are more likely to be irritated by websites which require plug-ins, scripts and high bandwidth simply to display a bunch of text.
Do your design as well as you please, but try to keep it as minimal as possible on bandwidth, plug-ins and scripts.
(Note: My own personal settings aren't the main topic of this answer, but as several people have made noises of shock at my default blockage of scripts, I'll clarify: I don't block first party scripts that are served by the actual website I'm visiting.)
Academia is full of people who are deeply passionate about their work but sadly are less than deeply passionate about making an effort to communicate effectively about their work to the rest of the world. That is a bad thing, not a good thing. That is why we see poorly written papers, poorly prepared talks, and why we see poorly designed (or nonexistent) personal websites. Moreover, many academics lack the technical skills and design sense needed to create a good website. Again, that is a bad thing (well, the sky won't collapse because of it, but you know what I mean).
Thus, I think the premise of your question falls into a logical trap of thinking that because something is the norm, it is good. That simply isn't the case. If you know how to build a really good website, and care sufficiently about making your work known and understood by others to spend the time doing it, by all means -- do it (and, of course, if you know how to write really good papers and give really good presentations, do that as well!). Be a leader rather than a follower, and show people the way to improving this somewhat pathetic aspect of academia. It will be a great investment of your time and a good way to set yourself apart from your (perhaps equally talented but less web-savvy) peers, as long as you don't go overboard and spend so much time on the website that it will seriously impact your research productivity.
For what it's worth, I'm not here to promote my own work so I won't include a link, but Google will show you that I at least try to practice what I preach.
Edit: To clarify, as far as the OP's literal question is concerned: no, academics generally do not look down on well-designed academic websites. As I explained above, in my humble opinion you have everything to gain and virtually nothing to lose by putting in a reasonable amount of work to build a clean, nice-looking website that effectively communicates to the world what you and your work are about. Moreover, by doing so you will be serving as a good role model for others and advancing the culture of academic dissemination of knowledge. At least one academic (yours truly) definitely approves of that.
Well-designed isn't quite the same as appropriately designed. A simple example demonstrates this:
An academic puts up a publications page with links and full titles/author lists, everything on one page. It takes a bit of scrolling to get to the bottom, but find-in-page can instantly show you whether they've written with a certain co-author, or used certain keywords in the title. But the page looks old-fashioned (raw html) and the lines are too wide on modern monitors.
The university forces¹ everyone onto pretty, standardised webpages through a CMS. Line lengths are optimised for reading, but there are only 10 publications per page, and author lists are truncated with "et al." automatically. No "search this author's publications" feature is implemented to make up for it.
Which would you rather use if looking up a potential collaborator? (If the academic keeps on top of such things, ORCID or ResearcherID can make up for this, Google scholar generally can't unless their name is very rare)
¹They turn off the server hosting the old pages and anything else they don't lock down, so anything non-standard wouldn't be on the university's domain.