To give any support for interpretations where transitivity comes out looking like a classification of verbs is going to get us into trouble and potentially confuse (or mislead) those just beginning, surely.
So, to get a dig in at Brad, doing transitivity analyses by swapping verbs is, well, well down that path …
On the one hand, this is the opposite of what is true, since, if two verbs are interchangeable in a clause, then it is the Process function of the clause — that either serves — that is being identified, rather than "a classification of a verb".
On the other hand, there are instances where "swapping verbs" is recommended as the 'best strategy' for transitivity analysis. Halliday & Matthiessen (2004: 233):
With a verb other than be it is clear which is Token and which is Value, since … this can be determined by the voice: if the clause is ‘operative’, the Subject is Token, whereas if the clause is ‘receptive’, the Subject is Value. … With the verb be one cannot tell whether the clause is ‘operative’ or ‘receptive’; the best strategy for analysing these is to substitute some other verb, such as represent, and see which voice is chosen.