Am I missing something?

charging up a R/C/LED circuit at V_cc is very much like charging up a R/C circuit with V_cc-V_fwd where V_fwd is the forward voltage of the LED.

So 63% of V_cc in this case (about 3 V) should really be compared to time constant of 3 V under a V_cc of 5 V - 2.2 V = 2.8 V < 3 V. Which is very very long, as you observed.

Am I missing something?

charging up a R/C/LED circuit at V_cc is very much like charging up a R/C circuit with V_cc-V_fwd where V_fwd is the forward voltage of the LED.

So 63% of V_cc in this case (about 3 V) should really be compared to time constant of 3 V under a V_cc of 5 V - 2.2 V = 2.8 V < 3 V. Which is very very long, as you observed.

edit: here is a quick simulation that may help explain the difference between a rcled and rc circuit.

The circuit on the right is a rcled being charged up at 9v. the circuit on the right is its equivalent rc circuit being charged at Vcc - Vfwd. The curves are roughly the same - but not exactly due to the much higher equivalent resistance of the led as charge current slows down.

hope it helps visualize it for the OP.

Am I missing something?

charging up a R/C/LED circuit at Vcc is very much like charging up a R/C circuit with Vcc-Vfwd where Vfwd is the forward voltage of the led. so 63% of Vcc in this case (about 3v) should really be compared to time constant of 3v under a Vcc of 5v-2.2v = 2.8v < 3v -> very very long, as you observed.

Am I missing something?

charging up a R/C/LED circuit at V_cc is very much like charging up a R/C circuit with V_cc-V_fwd where V_fwd is the forward voltage of the LED.

So 63% of V_cc in this case (about 3 V) should really be compared to time constant of 3 V under a V_cc of 5 V - 2.2 V = 2.8 V < 3 V. Which is very very long, as you observed.