Great primer. Two things that helped me actually internalize memorylessness when I first hit it:

1. The variance equals the mean, which most intros skip. For block intervals with $\lambda$ = 1 per 10 min, the mean inter-arrival time is 10 min and the standard deviation is also 10 min. That's why on any given day the gap between blocks can swing from a minute to an hour without anything being "wrong" — the noise floor is enormous relative to the signal.
2. Why memorylessness has to be true if we accept independence of hash attempts: every nonce trial is an independent Bernoulli with success probability $p=1/d$. The number of trials until success is geometric, and as $p\to 0$ with rate $h$, the continuous limit is exponential. Past failed nonces literally carry no info because each one was a fresh independent draw — there's no urn being depleted.

A practical consequence worth pinning to the wall: if you're a small miner and you've gone 6 $\times \frac{1}{{\lambda }_{\text{you}}}$ without a block, the probability you should have found one by now is $1-e^{-6}\approx 99.75\%$ — but conditional on not having found one, your expected wait from now is still $\frac{1}{{\lambda }_{\text{you}}}$. That's the part that breaks human intuition and convinces solo miners to pool up.