Well, without pollen-pistil incompatibility, there would not be distinct kinds of plants. The issue is not favouring or disfavouring gene transfer, it's a matter of preserving species and their distinct genotypes :)

Naturally possible with cross breeding through vectors like bees.etc.. Interm pollinators 

Related species tend to still be cross compatible; hence, horizontal gene transfer is definitely possible.

In line, the "gene pool" concept was created denoting the cross-compatibility of one species with respect to other species. Depending on compatibility, they are classified across different genepools.

gene pool concept: http://agriinfo.in/default.aspx?page=topic&superid=3&topicid=2101

See wheat genepool for example: https://www.researchgate.net/publication/270280504_Wheat/figures?lo=1&utm_source=google&utm_medium=organic

Corn as an example: https://link.springer.com/article/10.1007/BF00056581

Knowing that Corn and Tripsacum hybrids are possible, this indicates that tripsacum belongs to the secondary genepool of corn and, in nature, natural hybrids can be formed. Although, very few research deal with tree species.

In essence, natural interspecific and intergeneric hybrids between dioecious species do occur in nature.

Chapter Wheat