Transposable elements (TEs) are mobile repetitive DNA sequences that have been highly successful at invading eukaryotic genomes. TEs can be divided into classes, subclasses, superfamilies, and families depending on their replicative mechanism, ancestral origin, and sequence similarity highlighting the genetic and mechanistic diversity of TEs. The proportion of the genome occupied by TEs varies greatly between species, as well as how that proportion is distributed between the present TE families. Some TE families contribute relatively little to this overall proportion, with only a handful of copies present in the genome, while other families contain tens of thousands of copies. It is unclear how TE families reach a high copy number given the expectation that novel insertions be deleterious. Previous population genetic models have largely ignored the tendency of TE families to preferentially insert into specific DNA sequences or features. This insertion preference may not only be the result of structural differences between TEs but also an evolved trait that dictates an underlying distribution of fitness effects for each new insertion. It has been hypothesized that TE families may evolve a preference for neutral insertion sites to minimize their cumulative deleterious load and avoid driving the host population extinct. To test this hypothesis, we use a non-Wright-Fisher framework in SLiM 3 to explore how transposition probability and insertion preference influence the evolution of mean TE copy number and host population size. We consider a diploid population that gains a single copy of a TE in the genome of a single individual (analogous to horizontal transfer). This TE belongs to a unique family with an assigned transposition probability and range of fitness effects for novel insertions that represent insertion preference. We can track the spread of the TE family through the population by measuring its mean copy number and population frequency over time, and we allow population size to fluctuate depending on the fitness of individuals, such that populations can go extinct. Using our model, we find that population extinction occurs most often under high transposition probabilities, but, as we reduce transposition, we find that extinction persists when the neutral insertion preference is high, rejecting our initial hypothesis. Somewhat counterintuitively, a preference for neutral insertion sites allows the mean copy number of both neutral and deleterious insertions to grow most rapidly, consequently, leading to extinction. Our results show insertion preference is not protective on its own and suggest mechanisms that regulate TE transposition are key to obtaining high TE copy numbers.