I have always imagined that Hobbits "coming of age" at 33 is the equivalent, in our terms, of reaching the age of 21. This is the age at which people are traditionally said to have come of age in many of our societies. The symbolism of the key being handed over still survives in many Western cultures.
And, given the longer average life expectancy of a Hobbit (certainly compared to average life expectancy in the time that Tolkien was writing), I have always considered the age 50 to be nearer to 30 in human terms.
Not your typical youthful hero, admittedly, but still realtively young. And this accords with the picture painted of Bilbo, since it is in our 30s that we tend to settle down and become set in our ways (and I speak as a 30-something who has settled down and become set in his ways, and whose "Tookish side" is fading fast
).