I think there are two main points here:
Regards does not only, nor originally, mean best wishes .
In some particular contexts — most often, as closing salutations in letters or emails — they’re indeed effectively synonymous.
But regards has other meanings as well.
Originally, regards carried no specific connotations of being good ; it just so happened that one of its most frequent usages was for sending people kind wishes, and so in that context, it picked up those connotations.
Even if that were its only meaning, synonyms are not exact , and meaning is not substitutive — synonyms are very, very rarely so exactly synonymous that you can always substitute them for each other without changing meanings.
For instance, as synonyms go, puppy and young dog are pretty close — close enough that one might reasonably say “ puppy is defined as young dog ”.
(Indeed, checking a couple of dictionaries, it is.)
But a young puppy is not redundant:
we know it means (in most contexts) a dog that is young even for a puppy.
Nor is an old puppy an oxymoron.
In isolation, puppy means almost exactly young dog ; but it’s picked up different connotations, so in many contexts, replacing puppy with young dog can change the meaning of a phrase significantly.
This is why pleonasm is often rather effective: ‘technical’ redundancy can be an illusion.
Substituting synonyms to check whether something makes sense is often helpful nonetheless, as a very rough rule of thumb.
But when it doesn’t work, one shouldn’t be too surprised.
english.stackexchange.com/users/2587/PLL
a)
The answer to the question is No.
You might regard someone with a complete lack of respect !
So using regards alone doesn't clearly show how you feel about someone you're corresponding with.
Of course in correspondence using "regards" alone doesn't have a negative connotation and is used to show good wishes.
b) Sometimes pleonastic usage is welcomed.
The usages are: Idiomatic expressions
Professional and scholarly use Stylistic preference
Literary uses For getting more information visit Wikipedia
So for emphasizing or making the purpose clear we might use redundancies.
For example: "This was the most unkindest cut of all."
—William Shakespeare, Julius Caesar.
english.stackexchange.com/users/3782/Manoochehr
No, because I might regard you with disdain, or my worst regards.
english.stackexchange.com/users/588/Ed Guiness
Regards doesn't carry with it a very open and public sense of best that you're talking about.
Most people probably just understand it as something like "good wishes" or some other non-superlative and bland but positive way to express friendship.
So Best regards at the end of a letter, if it got noticed at all, would simply be read as equivalent to Best wishes .
english.stackexchange.com/users/2303/Robusto
You can also give someone kind regards, or warm regards, so specifying best regards is not redundant.
As PLL points out, "regards" by itself does not equate to "best wishes"; I think of it in this usage as "the worth or estimation in which something or someone is held" ( Merriam-Webster definition 4a).
In effect, you're closing with a little note letting the person know that you have a good opinion of them.
english.stackexchange.com/users/2490/Hellion
Regards is used to hide the emotional content of your salutation.
I once had a manager who told me there is no room for emotion in business, which I do not find to be true.
However, when needing to maintain a professional air surrounding emails and letters, regards is a snappy quick way of saying (more often then not) 'best wishes'; which therefore makes 'best regards' a redundancy.
english.stackexchange.com/users/37687/Chad Rappala
If the meaning of  regards  is  best wishes , would not  best regards  (used to express friendliness in greetings, especially at the end of letters) a pleonasm, in the context of letters?   Best regards,   kiamlaluno     Best best wishes,   kiamlaluno
Is "best regards" a pleonasm?
english.stackexchange.com
<phrases><pleonasms>
english.stackexchange.com/questions/11675
english.stackexchange.com/users/252/kiamlaluno
"Regards" does not only mean "best wishes", although in some popular contexts they are synonymous. "Regards" also has other meanings as well and carried no specific connotations of being good. Therefore, the answer is no, "regards" is not pleonasm. It is possible to give someone "kind regards" or "warm regards", so clearly "best regards" is not redundant. "Regards" does not only, nor originally mean "best wishes". In some contexts, as a closing salutation, the two words could be synoynyms. However, "regards" has other meanings, but it never had the connotation of "good" -it was just a form to close a letter. Even if it did have the connotation "good", synonyms are never so exact that they are  totally interchangeable. Since "regards" in a salutation, it does not denote one's feelings, you could still have little respect for someone and still sign off "best regards".  In contrast,  someone can sign of "regards" omitting "best" and think highly of their correspondent. "Regards" may be used to hidet the emotional content of the salutation; so therefore it's a quicker and more professional form than "best wishes!.  There are other options also, such as "warm regards" that could be used to express how highly you think of someone.
"Regards" does not only mean "best wishes", although in some popular contexts they are synonymous. "Regards" also has other meanings as well and carried no specific connotations of being good. Therefore, the answer is no, "regards" is not pleonasm. It is possible to give someone "kind regards" or "warm regards", so clearly "best regards" is not redundant. While the meaning of 'regards' has changed over time, in modern usage ending a letter or email with '(Best/warm/kind) regards' would be considered equivalent to 'Best wishes'.
Best regards is not a pleonasm, as you could be regarded with disdain, or my worst regards. No, "best regards" is not a pleonasm.
Does not equate to "best wishes" Regards does not show emotional content The notion of "best" is not contained in the salutation. Understood as good wishes, may go unnoticed and understood as "good wishes" Choice of form that can be used.  "regards" removes emotional content
While the meaning of 'regards' has changed over time, in modern usage ending a letter or email with '(Best/warm/kind) regards' would be considered equivalent to 'Best wishes'.
No, "best regards" is not a pleonasm.