There is a workaround, sorta. You can tell Siri to start a timer for a fixed period of time: "Hey Siri: one hour." It will faithfully start counting down. "Hey Siri: pause timer." It will stop. When your hands are free, you can pull it out of your pocket and do the math. Of course, you have to predict how long you'll want it to time so it doesn't stop timing when the timer runs out.
You can also say "Hey Siri: take a memo." Your memo can reflect what it is you wanted to time, and it will put a timestamp on the memo, so you'll know when it happened. Then you can do the math later for that, too. Of course, you have to also take a memo for when you stop, etc., and calculate the difference.
If they ever do enhance these features, not only should they allow stopwatch functions, they should also allow you to create multiple stopwatches and or timers on the fly and name them. That way, you'll know what they were when you look at them later. ;-)