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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 ...