Sure it will be hard to determine if the improvements are due to the cause of SEO or some other update, but using revenue as a metric has the same issue.
(Ideally one would use a "difference in differences"[1] approach, but it could be difficult without good comparators).
However, there is another problem with metrics. Sometimes, it is too easy to pay too much attention to vanity metrics that won't add anything to your bottom line. Will moving from a 25th place to 1st place for a search help your business? That depends - does that search generate traffic, and does that traffic generate revenue? On the other hand, increasing revenue is never a bad thing.
I'd argue that unless decision makers have too much time on their hands, they're better off focusing on metrics like revenue than metrics like search results. Validity will be a problem across all metrics, but at least there isn't a tendency to optimize useless metrics.
I think that's what the previous poster is getting at - getting a lot of revenue isn't hard if you're willing to throw core parts of your business under the bus (say, profitability).
More generally though optimizing for any kind of financial target (whether revenue, profit, or otherwise) can still be gamed like any other metric.
Your salesperson promises the moon to a client, closes a bunch of deals, looks great, and your company takes on a boatload of liability in the process - for example.
Or, to take a real life example - drop the price of your software to 99 cents and ride a huge sales wave but find your clientele unwilling to pay anything more than 99 cents from then on (hellllo mobile apps).
Lots of ways raw revenue/profit isn't by itself a great metric.
Oddly I was reading how Buffets first insurance company was focused on writing profitable premiums only - to the extent of seeing shrinking business. It was unusual then and now, so I do take your point.