Theoretically, it could have. There have been Android apps that replicate this functionality for years, but of course Apple doesn't let third-party apps play with incoming phone calls beyond a few specific (and recent) APIs that allow for things like spam call detection and blocking.
Apple has chosen not to do this, and there are probably some valid reasons why it would have wanted to avoid this. Early iPhone models may not have had the performance to handle it properly, but the biggest issue is that having the phone answer the call requires that it actually be able to receive calls.
Standard voicemail works when your phone is dead or out of coverage; this new Live Voicemail won't, but at least you'd have a "real" voicemail box to fall back to in those situations, and Apple appears to be doing this as seamlessly as possible — at least if you're using a custom greeting, your callers won't know the difference. That's a stark contrast to Google's call screening, which puts the person into a conversation with Google Assistant asking them to explain why you should answer their call. It's also why I suspect Apple may tie Live Voicemail into having VVM; I'm really hoping it doesn't, but Apple is all about the user experience, and the average user may have a hard time understanding why their callers don't get their voicemail box every time they can't answer.
As for why Visual Voicemail costs more, that's due to the "visual" part of voicemail that Apple cooked up — and bear in mind this has been around since the original iPhone launched 16 years ago. This requires special software on the carrier's voicemail servers to download and synchronize the voicemail messages directly to the iPhone over a data connection. It's a lot faster and more reliable than having the iPhone automatically dial into the carrier's voicemail service the old-fashioned way to playback and record the messages onto the iPhone, which would be the only way Apple could do this without setting up special Visual Voicemail services with the carriers. That would end up being a nightmare considering that every carrier uses a different set of menus, prompts, and touch-tone numbers to access voicemail messages.
Sadly, I think Apple's original vision for Visual Voicemail didn't pan out the way it had hoped. AT&T didn't charge extra for VVM with the original iPhone — it was all part of the "iPhone plan," which also included unlimited data for the first time ever. Sadly, as other carriers got their hands on it, they saw it as another money-making opportunity and started charging for it as a value-added service, often at a higher price than "basic" voicemail. Apple had to fight the battles it could win if it hoped to get the iPhone sold around the world, and it held its ground in more important areas, like refusing to allow carriers to sully the iPhone with their own branding and bloatware.