I created a sentence earlier today stating "他是一点儿严厉," but I was told that it was better if I say "他有一点儿严厉”。They didn't really know why, but just that it made more sense - could someone elaborate when to use 有 vs 是 in the sense of describing objects with adjectives? Hopefully what I'm saying makes sense :)
有(一)点 as a set can use to mean "a little too...". See this Chinese Grammar Wiki page.
Some examples from the page:
我 有点 饿 。
I'm a little hungry.
这个 菜 有点 辣 。
This dish is a little too spicy.
昨天 有一点 热 。
Yesterday it was a little too hot.
是 does not have this usage, so 他是一点儿严厉 is wrong.
However, you can say 他是有一点儿严厉, where 是 is used for emphasis.
一点 makes 有 valid. According to dictionaries, one of the usage of 有 is to describe extent (how large, how big, how severe, etc.). E. g. 他有两米高. (not 他有高). In your case, 他有一点儿严厉 makes sense, whilst 他有严厉 does not because it doesn't specify the extent(一点儿).
是 + adj is used for emphasis, denoting the sense of really or indeed. E. g. 他是严厉(he's indeed strict)。他是聪明(he's indeed smart)。We put an emphasis on 是 when we say those sentences, or they might sound wrong.
@fefe's answer about 有一点 as a set is correct. It is of course colloquial only.
There is one more thing.
When you compare 是 to the English be, 是 is only used in predicative statement. (Such as the exact one I just used.) 是 is not used as the universal linking verb before a descriptive adjective.
"He is strict" in English attaches the adjective "strict" to the object in question "he" as a linking verb. 他是一点儿严厉 breaks up the colloquial word phrase 有一点儿。But moreover, 严厉 is not used as an adjective that requires linking verb. (严厉 is a descriptive quality. But that does not make it adjective in the same style as in English. Semantic does not mandate syntax.)
是 is indeed used for emphasis as @fefe mentioned. That often places 是 in the same place as the English "be" even when the function of 是 is not as a linking verb. For example, 他是严厉 is used by Chinese speakers and is better translated as "that he is strict" or "he is indeed strict" depending on the context to give emphasis or affirmation.
有一点 is colloquially almost as if "is a little" in English -- ie. containing an inferred linking verb. That explains 他有一点儿严厉
是 is not a universal linking verb for adjective. 是 is not used for comparative adjectives. It is comparable to the English "be" only in 1) predicative statements, 2) for special emphasis, 3) as linking verb for words modified into adjective using ...的.
有 vs 是 are not comparable per se. (Though the usage of 是 deserves considerations and clarifications along the line of this thread. So good question.)
EDIT: incorporated user21820's comment.
In Chinese there are verbal adjectives.
I am tall. 我高。not 我是高。
高 is a verbal adjective here. It does not mean ''tall'', it means ''to be tall''. So the verb 是 is not used with verbal adjectives.
Here are some other examples.
我严厉。我饿。我累。我胖。 Get the idea ?
Now , in Chinese to say ''a little'' is 有点儿 or as you've put it 有一点儿。
The 是 is built into the verbal adjective 严厉, and 有 is part of the 点儿 structure.
If you want to say ''I am indeed something'' in Chinese then you would add the 是 and emphasise it when speaking.
I am indeed tall. 我是高 or 我是很高。
I am indeed a little bit stern. 我是有点儿严厉。