A recent Reddit post posited that Apple was intentionally slowing down iPhones with low-capacity batteries. And that same post concluded that most iPhone users whose phones have slowed probably attribute it to iOS updates.
A number of people (including the original poster) confirmed that when they did replace their batteries their phone performance and CPU clock speeds returned to normal. As pointed out by The Verge, this is relevant (especially if you have an outdated iPhone) because users whose phones slow down are probably tempted to pony up their dough for an unnecessarily expensive upgrade.
Additionally, The Verge reached out to Apple for comment, and when they did so the company pretty much confirmed the discovery, though they simultaneously denied that their motivation was greed. As Apple said:
Obviously Apple is saying they're attempting to address an issue with phones randomly shutting down as they age, especially in extreme temperatures. The issue seems to be one that comes from Apple not being upfront about their phone slowdowns, and thus a conspiracy theory was born, which makes sense since opacity is probably the No. 1 reason for most conspiracies. If you currently find yourself in the market for a new iPhone solely because of your current one's performance, keep this in mind.