The mess in Texas was caused by not having enough reserve capacity to cover a period of exceptional demand, technical failures at power plants caused by extreme weather and under-investment, and not having sufficient interconnections with the rest of the North American grid which would have allowed more power to be imported.

These problems are independent of whether you're operating a market model or a monopoly model. The market model is common throughout Europe, but widespread power shortages don't really happen because there are many interconnections between countries, and mechanisms (such as payments made to reserve generators based on their availability) which prevent market failure.