Interesting question. Are you referring to the fact that there is only one active subfamily of L1 at any given time? Or that there are not more type of autonomous retrotransposons (Ty1 and L1) within the same genome? The first wouldn't have so much to do with host factors as it does with the nucleotide mutation rate (will explain more if this is your question).  The second is somewhat a misnomer. There are multiple autonomous retrotransposons in human, they are just of the Long Terminal Repeat class (endogenous retroviruses)

I think 

Article Environmental Stress Activation of Plant LTR-Retrotransposons

Also Epigenetic play a great role in that. See attached

Article Epigenetic activation of genomic retrotransposons

Very interesting question. It may depend on the niche each transposon exploits.  For example, speaking of targeted sites for insertion, high redundancy may tolerate multiple lineages. However, I think different explanations can be invoked for different situations; it would be interesting to review all known  transposon niches to see if a greater picture emerges.

Although a family of L1 LINEs (retro-TEs) appear to be only autonomous TE currently active in humans and other primates there certainly have been LTR retro-TEs active in the not too distant past, concurrent with L1 LINEs. Prior to about 40 Mya there were active DNA-TEs concurrent with active L1 LINEs, as there still are in bats today. TEs usually have a limited lifespan in any one lineage, as they gradually accumulate mutations and eventually all become inactive, as L1 LINEs have done in some mammalian lineages. It appears that only viable (active) TEs can be horizontally transferred from lineage to lineage, so autonomous TEs get a fresh start in a new lineage , but once again they gradually (100 Myr ?) decay until they all become non-viable within the new lineage. LTR retro-TEs are different, as they can be derived by the loss of the env gene by endogenised retroviruses.

This is a rather simplified answer to a very complex question, but it should help a bit. You would do well to read the papers I have co-authored which will give you more imformation.   

Wow, thanks a lot for the many good answers, additional material and inspirations. I think I have to dig a bit deeper into the topic. It would be interesting to see if the lost L1 activity in some bats and rodents has any consequences for other autonomous elements. The landscape of L1 depending SINEs will definitively change over time.