Lychee:

There is no obvious reason why this cantaloupe/honeydew cross from Israel should behave differently from other melons of similar type.

You can eliminate the seeds as a suspect for the dry mealy quality of your melons. Seeds either germinate or don't, and after that it is up to the plant and the grower to supply conditions that will enhance melon quality. This is assuming, of course, that the seeds were purchased from a reliable source of quality seeds, and not something someone saved from last season.

There is no single cause that is responsible for all the dry, mealy melons that are grown in this world. It is more likely the whole package of conditions under which your melons were grown, including soil, sunlight, and possibly water. You don't tell us much about how your melons were grown, so it is difficult to judge the influence of any one factor over another.

Don Yellman, Great Falls, VA

Thanks Don.

I grew them up a trellis. I guess I will try again next year.

I grew some really soapy GALIA melons. They were grown right next to plants bought at the nursery, which produced quality melons. The seeds of the Galia were from Territorial Seeds, generally a good outfit, but which will occasionally misfire.
It happens, no hybrid you can find on the Internet is truly 100% guaranteed.

Glib:

I don't think much of Territorial Seeds, and stay out of their territory. I just rebel at organic preachiness. Nearly all my garden seeds are purchased from Stokes Seeds, a truly professional outfit that serves the market garden trade. They can't afford to sell questionable seeds, and in my experience they never do.

Don Yellman, Great Falls, VA

I understand. They also sent me a large packet of Tom Thumb lettuce where not a single seed sprouted. But, coming from Zone 8 to Zone 5.5, they helped me quite a bit with getting my northern garden organized. Their staff is very helpful. Several of their northern varieties are superb (my garlic has spread out to friends, family, family of friends, and friends of family), and the hoophouse clamps they sell made it possible to have vegetables 11 months a year without too much sweat.