Can I get away with only owning either a metric or 'American/SAE set of tools?

Likely to only own vehicles
Currently own 05 Chrysler Town & Country and 05 Ford Freestyle don't have lots of $ to by 2 of ea. Set

Even if you only own American made cars they are almost guaranteed to have both SAE and metric bolts. Go to Harbor Freight and buy a set of whatever ones you need along with a couple of torque wrenches in 3/8 & 1/2" drives. Get on their mailing list and receive coupons every month to save even more.

https://www.harborfreight.com/

No.
Most cars have a mixture.

Depends what you use, if you start repairing other's cars metric is gonna be more useful, but some cars even mix and match the two. My Imperial (SAE) tools spend most of their time their rolls, but yeah I couldn't do without it

Need both

I've used metric tools for 35 years on both imports and American made vehicles. I've purchased several deep impact sockets for removing axle nuts that are specifically for American made vehicles. Buy the metric tools.

'05 American cars are all metric. But, 1/2" is close to 13mm, and 15 I think to 9/16:.

I don't have a lot of samoleans, either, I have my Daddy's old Craftsmans. But, believe it or not, Harbor Freight tools are improving. Get a set on sale. You won't need a lot, just 3/8" ratchet and 6-point sockets, combination wrenches, screwdrivers, occasionally a torx or two. A #3 or #4 torx screwdriver ( I ferget exact size) for spark plug changes on the Chrysler.

Most are a combination of BOTH.

No. Even most "American" vehicles these days use metric fasteners in their construction. If you can't afford to buy a proper set of tools to work on your car, then don't buy a car.

Most American vehicles use metric fasteners nowadays.

Your cars are metric this has been true for at least 20 years.