Knuth's up-arrow notation - Is there practical use for the numbers involved?

From Wikipedia, Knuth's up-arrow notation begins at exponentiation and continues through the hyperoperations:

$a \uparrow b = a^b$

$a \uparrow\uparrow b = {\ ^{b}a} = \underbrace{a^{a^{.^{.^{.^{a}}}}}}_b$ (the tetration of a and b; an exponentiation tower of a, b elements high)

This already produces numbers much larger than the number of Planck volumes in the observable universe with very small numbers; $3 \uparrow\uparrow 3$ is a relatively modest 7.6 trillion, but $3 \uparrow\uparrow 4 = 3^{7.6t} = 10^{3.6t}$.

Then there is pentation ($a\uparrow\uparrow\uparrow b = a\uparrow^3b$) and hexation ($a\uparrow\uparrow\uparrow\uparrow b = a\uparrow^4b$). The pentation of 3 and 3 is $\underbrace{3^{3^{.^{.^{.^{3}}}}}}_{\ ^{3}3}$, an exponentiation tower of 3s 7.6 trillion elements in height. Hexation is an exponentiation tower of 3s equal in height to the value of the pentation of 3 and 3. And that is just $g_1$, the first layer of calculation necessary to compute Graham's number, $g_{64}$, where $g_n = 3\uparrow^{g_{n-1}}3$.

I'm having considerable, and I hope understandable, difficulty simply wrapping my head around a number of this magnitude. So, the question is, is there value in understanding the scope of numbers produced by Knuth's up-arrow notation, or is this simply a way for mathematicians to make each others' heads explode?

If it's the latter, I leave you with the following:

$A(g_{64},g_{64})$

Yes, see "Enormous Integers in Real life" by Harvey Friedman.