I didn't know Alphabay, it was a bitcointalker from the local French forum who mentioned it. Given the fate of Ross Ulbricht (imprisoned then recently released against all odds) and Alexandre Cazes (dead at 26), whose businesses lasted around 2 and a half years each before the final downfall, I wondered why they didn't stop sooner, when they were already very rich.

What motivates these people, who have become criminals, to continue their business when in the end they live in extreme danger?

Initially, they were not particularly disadvantaged (which sometimes could explain the choice of a criminal path) and, unless I'm mistaken, they are quite intelligent and could have embarked on a successful career.

Here are a few hypotheses :

1. Ideology and Libertarian Vision (for Silk Road)

Ross Ulbricht (Silk Road) was not just a criminal looking for money (I just saw a documentary and some witnesses, including his girlfriend at the time, say that one of his objectives was clearly to make as much money as possible). He saw his site as a libertarian revolution, a way to bypass government control and enable free and anonymous trade.
He believed in crypto-anarchism, where Bitcoin would eliminate banks and regulations.
He kept going despite the risks, thinking of himself as a pioneer of a world without government surveillance.

2. Addiction to Power and Control

At a certain point, it was no longer just about money but power. Running a darknet empire provided an immense psychological thrill and a sense of being untouchable.
Criminals like Ulbricht and Cazes must have tought they were too smart to get caught.

3. The Illusion of Invincibility

As their sites grew, they believed they had perfected their anonymity and security. Ross Ulbricht thought that his use of Tor and Bitcoin made him impossible to track.
Alexandre Cazes was living a luxurious life in Thailand, convinced that law enforcement would never catch him.

4. Greed and the Difficulty of Stopping

Even though Ulbricht was motivated by ideology, he was earning millions of dollars in commissions. Cazes, on the other hand, was clearly money-driven, owning luxury cars, villas, and millions in crypto.
When running an illegal platform generating millions per month, it’s hard to say, “I’ll just stop and walk away.”

5. Business Pressure and User Dependence

Once their sites were running, shutting down meant losing all control and risking leaks of information. Darknet vendors and buyers depended on them and expected reliable service.
A site like AlphaBay or Silk Road couldn’t be sold like a traditional business, so the only way out… was often getting arrested.

It would seem that money isn't everything, and that even the richest criminals keep on doing what they're doing until they're caught or killed.

They seem to love power and adrenalin; for some, fear is part of everyday life and not a problem.

I think it's a risky life that's hard for parents to accept (when you're not a criminal yourself).