Presumably in a large sample (here being cases, not people), some will be statistical ties and some not. For example, the senate is in a statistical tie, as is Pennsylvania and Brazil, and many others, but the house isn’t, nor is Montana, etc., etc. We tend to notice statistically tied races (and settings) because they are where swings happen, so they are important but a statistical tie seems so unlikely that having one would seem unstable, yet they seem to persist for long periods (e.g., most swing states remain swing states for many elections). Is there some force keeping these pencils balanced in their points, or is this merely a perceptual selection bias?
There does seem to be a lot of close elections, don't there? But this is partially an example of selection bias, partially the nature of politics (and the U.S. system in particular), and partially the limitation of polling:
Limitations of polling: There is no widely agreed upon meaning of "statistical tie," and actual pollsters and statisticians don't really like the term. The media typically use to mean it falls within a poll's margin of error. But that means a 49%-43% result with a 3.1% MoE is actually a "statistical tie," even though in all likelihood candidate A is beating candidate B rather soundly. And unsurprisingly, media outlets like to take every opportunity to portray a race as closer than it is to keep people tuned in.
Selection bias: You mention that the U.S. Senate and the Pennsylvania Senate races are tight, while the House is not. But the U.S. House election is really 435 distinct elections, and the Senate election is around 30. RealClearPolitics indicates that only seven of the Senate races this year are toss-ups as of this writing, and only 33 of the House races. What that really means is there are four hundred or so races where the results are not close at all. Naturally, neither the media nor politicians focus on the races that are foregone conclusions.
Nature of politics: Parties and politicians are rational actors who want to maximize their chances of winning elections. In the U.S. in particular, most candidates run in a first-past-the-post, winner-take-all system. That means there is no benefit to coming in a respectable second and you pretty much have to shoot for 51% of the vote (or 51% in 51% of the districts) to gain power.
This highly incentives a two-party system and moderation towards the mean voter. That in turn tends to naturally result in races that are deadlocked as both parties are entering a contested race with the candidate, platform, and messaging they believe gets them closest to 51%.
If both parties were pouring their resources into Pennsylvania and the polling was 60%-40%, that's a sign someone horribly miscalculated. And hey, that does happen. But the game never stops gets played and parties can correct their mistakes in later rounds. The U.S. is now in Round 118, and the players have gotten pretty good at it.