Should I sell if a stock cuts its dividend?

Dividend strategies are popular amongst UK investors. The ability to receive a market-beating passive income from simply holding large, steady companies is incredibly attractive to those who use their stock portfolio to help with living expenses. There is evidence that this kind of Value strategy beats the market over the very long term, although perhaps by less than other value strategies.
Towards the end of 2022, I wrote an article proposing a Value-first strategy. I suggested investors would be better off screening for stocks that meet Value criteria first and then picking a diversified collection of the highest-yielding stocks out of these. However, when I reviewed this strategy in 2023, the results were a little disappointing. What I called the “Safer Income Portfolio” beat some other simple value strategies. However, it underperformed the FTSE All Share, at least on price-performance:

More disappointingly, the portfolio contained four companies that cancelled their dividend payout:

And some that cut their dividend while not completely cancelling it:

It seems that this income portfolio was not safe enough, and in...