The technical limitations of using the DOI as bibkey are that they should not contain a character that has special meaning in the
.bib file syntax, that is you cannot have a comma
, or curly braces
} because that will make Biber/BibTeX think the bibkey has ended when it hasn't.
Additionally one should be wary of special UTF8 characters in bibkeys (see How to have special characters (e.g. german umlauts) inside bibkeys?) which are certainly possible by the DOI standard (see DOI handbook)
DOI names may incorporate any printable characters from the Universal
Character Set (UCS-2), of ISO/IEC 10646, which is the character set
defined by Unicode v2.0. The UCS-2 character set encompasses most
characters used in every major language written today.
The Handle System at its core uses UTF-8, which is a Unicode implementation and so in its pure form has no character set constraints at all: any character can be sent to, stored in, and retrieved from a handle server. The IDF imposes no additional character set constraints. In practice, though, there are many character set constraints enforced by the current web environment, depending on the individual user's context — for example, what kind of browser is being used.
Except for the specific requirements imposed by this standard (such as use of Unicode and reserved characters), no restrictions are imposed or assumptions made about the characters used in DOIs.
So you cannot be sure that you can actually support all possible DOIs in bibkeys because of LaTeX/
biblatex's technical restrictions.
In real life, however, you will probably struggle a bit to find a malicious DOI - a major part is benign and only contains digits, lower case letters, dots and slashes; but then there are beauties such as
where Biber refused to compile because of the parentheses, BibTeX ploughed on happily, though.
In a nutshell, the DOI standard does not prohibit problematic DOIs that might cause havoc in the file, and while most DOIs out there today are totally fine there are already some that are troublesome.
"Human Factors and Ergonomics (and Mnemonics)"
In an ideal world bibkeys are easy to remember and recognise such that someone who sees the bibkey immediately knows what work it refers to - or at least has a rough idea.
Bibkeys containing the author name, a year, some leads on the title in the form of the most important word or initials are arguably easier to remember and give a better primer of what the work might be about - a DOI will be helpful in this regard only to very, very few people (but there are auto-complete features and bibliography integrations for editors so that this can be remedied up to some point).
In a nutshell, DOIs are very abstract and (almost) devoid of any meaning for humans thus inhibiting an easy grasp of the works cited from seeing just the bibkeys.
The undeniable plus side of using DOIs is that we are guaranteed to be collision free.
Most other (more human readable) formats have a risk of suffering from some form of collision.
You could either go down the route of choosing one of the following formats suggested by egreg and jon
<name>+<year>+<prominent word in the title/important concept of the article>
<name>+<year>+<first letter of the first n words>
Of course none of these are guaranteed to be unique, but they come close. (Some editors provide facilities to auto-generate some forms of keys and check uniqueness in the database.)