Yes, $30 is an insane estimate for the cost of a PID controller. Probably because nobody buys discrete PID hardware anymore because microcontrollers disrupted that market decades ago.

You could easily implement thousands of PID controllers sufficient for this application on a $3 microcontroller with a $2 thermistor. Those are sparkfun prices, so 1/2 that would not be unreasonable for a BOM estimate. Sundry connectors and power transistors would cost more, but those will be present in the analog version as well. Temperature proofing is unnecessary - the sparkfun thermistor is rated to 125C and you can trade latency for max temp by moving it away from the heated parts. In this application you can afford to trade truckloads of latency.

Also, this is not a project for 3EEs + 2 technicians, this is a project for 1 bored EE in an afternoon. I suspect calibrating the digital version would be 10x-100x easier on an industrial scale.

I have no idea why or how he thinks the analog version would work better, so I can't really counter-argue.

The PID controller was definitely the part that stuck out to me. To me, a PID controller is a method of designing a controller and thus essentially "free" to implement in software. Do you happen to know where this $30 number comes from? Also, I highly doubt that there's much variation in the "PID quality". This isn't a use case that should require especially careful controller design/tuning; it's not like your water temperature is going to see large sudden fluctuations.

On a separate note, the price jumps from $16 to $45 going from the analog to digital version, though as far as I can see the only digital-specific additions are the EEs ($7) and PID controller ($10).

On DigiKey I can find a bunch of PID controllers in the >$200 range. I suspect that the $30 figure comes from a discrete package that made economic sense long ago when one had to use op amps and tuning pots to build a PID circuit. Even though microcontrollers have disrupted that market, the ancient PID controllers will stick around in supply warehouses as long as the machines which used them need replacement parts. $30 (or $200) could be significantly above the original manufacturer price if the parts are no longer manufactured but are still in demand. If one has only ever heard of PID controllers as "the semi-magical black boxes used to solve control problems" then one might make the mistake of only looking through the purpose-built controllers rather than looking for the cheapest uC.

As for your separate note, I noticed that inconsistency as well. I never figured it out, although by that point I was ~70% sure the whole analysis was botched so I didn't spend too much time thinking about it.