Yes, it is not trivial to define what a word is (I am well aware of that), but the fact that it is difficult does not make it impossible to make quantitative comparative statements about the number of words a language has. It is also difficult to exactly define and measure GDP, yet nobody raises that facile methodological objection when we say that Singapore has a higher GDP per capita than Swaziland.

Now, one can basically create an infinite number of words in some languages with compound words (eg German) and agglutination (eg Turkic or Uralic languages); it makes sense to exclude those (to avoid counting infinities).

Here's a source (from a collaboration between Dictionary.com and Oxford University Press) that basically concurs that English is the language with most words (excluding the results of agglutination):

https://www.lexico.com/en/explore/does-english-have-most-wor...

EDIT to add language (family) examples and this:

Here is The Economist with the cop-out answer that it's difficult to count:

https://www.economist.com/johnson/2010/06/23/the-biggest-voc...