Husk, 12 bytes

►=fImLmf√ġK√ 

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From Zgarb:

► has a second mode. If you give it a binary function f, it returns an element x that maximizes the number of elements y for which fxy holds.

So ►= is a 2-byte max by frequency.

Explanation

►=fImLmf√ġK√ ġK√ group string on non alphabet-characters. f√ filter out non-alphabet characters m map that to each word ↑ mL Length of each word fI filter out zeroes (empty string length) ►= max by frequency 

Husk, ¹² 8 bytes

►=mLmf√w 

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Previous answer was badly optimized.(-4 bytes)

From Zgarb:

► has a second mode. If you give it a binary function f, it returns an element x that maximizes the number of elements y for which fxy holds.

So ►= is a 2-byte max by frequency.

Explanation

►=fImLmf√ġK√ ġK√ group string on non alphabet-characters. f√ filter out non-alphabet characters m map that to each word ↑ mL Length of each word fI filter out zeroes (empty string length) ►= max by frequency