Do different match types really "compete against each other"  I would think not.  Are you really saying if theres:  [some keyword] and +some +keyword  that Adwords won't only send the closest match type to the auction and ignore others, or, if the bid for [some keyword] is $1.00 and for +some +keyword is $10.00 then you are effectively bidding $10.00 on some keyword.  However this is rare someone would make the broad match bid higher than a closer match type, so in reality I don't see a realistic scenario where a broad match is "competing" against an exact match  to effectively raise the CPC.    If the broad match bid was $0.99 and the exact match was $1.00 the exact match still goes to the auction with $1.00 max CPC.  You only send one keyword to the auction correct?

I want to be clear that I'm not referring to a re-crawl, but a re-index.  Now I realize there are a gazillion ranking signals and most of the stronger signals are probably not on-page signals (although page title, headers, and anchor text combined is probably a relatively strong signal) so that for most situations, on-page changes are going to like move you from the middle of page 2 to top 3 (except for obscure - low competition long tail keywords of course.)

So is there a delay between re-crawl and re-rank (I'll use that term instead of re-index).  I also realize the rank can change based on changes on the other sites in the SERPS.  I suppose the re-rank delay could be verified by taking a 'sacrificial' page and totally changing the title, headings, and other on-page items to a completed different keyword theme and see how long it takes for the rank to go down for the previous keyword theme and up for the new theme.

I would think Google would quite possibly add a delay, even a random delay length, to discourage people from constantly requesting re-indexing of a single page to see the rank change.  Granted the change if any would be small since on-page signals as I mentioned are a sliver of the signal pie.  So most SEO's I would think would be of the opinion this 'trial-and-error' is a waste of time?

In Google Search Console, when you request the (re) indexing of a fetched page, what's the average amount of time it takes to re-index and does it vary that much from site to site or are manual re-index request put in a queue and served on a first come - first serve basis despite the site characteristics like domain/page authority?