The above is pretty much the opposite of my experience growing Bradford watermelons this year. They are more variable than I anticipated and do have several flaws. They would not hold up compared to highly selected commercial watermelons today. Many of the Bradford watermelons had white streaks through the pink flesh. The rind is thicker than normal and bred so that it does not split. Overall flavor ranged from good to very good to excellent. Two of the Bradford watermelons I ate this year would have classed in the top 5 watermelons I’ve ever eaten. They are distinctly vigorous continuing to make melons for about 2 months. IMO, growing conditions make a world of difference with watermelon flavor. I grew them in sandy loam that has not grown watermelons in at least 40 years. Castanea is correct that they have a relatively short window to pick at perfect ripeness.
Here is what I posted in the current watermelon thread: