My memory is not perfect, but last year members of one of the bee associations to which I belong installed around 125 packages last spring. About 17 packages absconded, and they were about evenly divided between hives with solid bottom boards and those with screened.
I doubt the open screen bottoms are the only cause of packages absconding, but given my choice I would install a package with the screened bottom closed. Small colonies do better in small hives with small entrances, unless the outside temperature is very warm. Early spring temperature is usually cool enough to require the beekeeper to "baby" a 2 or 3 pound package.
With the problem wide spread as it appears to be, when installing packages I would take the precaution of placing a queen excluder under the brood chamber to prevent the queen from having free passage out of the hive. I would keep the excluder on the hive until the queen has several frames of unsealed brood. If brood from other colonies is to be had, I would add a frame of unsealed larvae when installing and 10 days later a frame of emerging brood.
I use screened bottom boards on all of my colonies, including my nucs. I never close the screen, even on the nucs. Granted, my winters are mild compared to northern states, but are no milder than winters in southern Missouri, Tennessee or other areas along Latitude 36. My winter losses are reasonable, if I have prepared properly. My style of beekeeping includes the use of powdered sugar dusting, which requires open bottom boards. I also see evidence that natural mite fall allows many viable mites to fall out of the colony. Fully one out of 5 or 6 are alive and mobile on the closure board when I do natural mite fall counts.
I am pro open mesh bottom boards because of the benefits I derive from their use. Others whose beekeeping style is such that they receive no benefits from their use would not like them, I can understand that. When I recommend a procedure or beekeeping method to a new beekeeper I do so because I have found it to work under my conditions. I do not know all of the conditions in other areas of the U. S., and I can't read minds, I can only tell what works for me. Also, I will have tried the item or procedure, or I will say that I have not tried what I am recommending.