Should I use a not-self-hosted website for both blogging and collecting academic materials? Several researchers in my subfield (and in mathematics in general) use not-self-hosted wordpress.com subdomains for their 'professional blog' (to blog about their research, their latest papers, or any topic related to their interests). Few of them use some pages of their blog as 'professional websites' too (to upload their CV, list of publications, material for courses, and so on).

I've made up my mind to start blogging myself; also, I'd like to create a webpage 'independent' from the one on a subdomain of my current institution (to make my life easier when I'll change place and to have some more flexibility). 

Should I use a not-self-hosted website for both blogging and collecting academic materials?

So far, these are the results of my research (in and outside my department) on the topic (but I'd like to examine some more objective and expert points):

"Pros"


I like that it is easy to use and set up (without any need to set up (and pay) your hosting yourself and actually "code" your website -- which would be hard since my knowledge of computer science and programming is very limited). Plus, some free themes are nice, essential, and easy to navigate.
I like the idea of connecting blogging and actual academic work.


"Cons" (i.e. the points that I'd mostly like you to address)


A friend of mine (who is not in academia anymore) implied that not-self-hosted websites look very unprofessional and cannot be fully optimized and personalized. Is the perception of not-self-hosted websites as unprofessional a real thing in the academic world? (In my opinion, on the contrary, seeing a website of the form namesurname.com could leave the impression of great pretense).
It has been pointed out to me (by a much senior researcher) that having "serious" (or at least would-be serious) research achievements on the same website as "more relaxed, informal, or expository blog posts" may be detrimental to the perception of the research itself. I strongly disagree on this point, but I'd like to do a reality check to see if this is actually a potential issue or just an "old-styled-man's viewpoint".
These subdomains and (mostly) the themes can be unstable (or be no longer updated/supported) and thus force me to redo the set-up at some point in time. Specifically, they may be more unstable than the website of a university. I really don't know about this, so I'd like to check, but I've heard it from a grad student in computer science.
In academia, an amateurish-looking website can almost be worse than having no website at all. Now "amateurish" here does not mean "made yourself"; it instead refers to sites that use bad design practices (lots of garish colors, ill-chosen animations and transitions, poor design choices that make it hard to find information). However, there is not necessarily a strong link between poor design and web host. So, you can and should decide if the web host makes sense for you.

I know a number of researchers who have their websites that are hosted by sites such as Google Sites, but they do look professional enough to pass muster. On the other hand, the main issues for a web site in academia is that you are able to find the information you need. A bare-bones text-based website (which many people still use) is perfectly acceptable if you can access a researcher's CV, lists of interests and publications, and get contact information.