Why does competition, cost, etc. vary so widely between broad match, phrase match, and exact match keywords?
The more general the match type of your keyword, the more risk you have of your ads being irrelevant or mismatched to your keyword choice.
Advertisers are often willing to pay more for relevant queries (exact match) versus generic or loosely matched terms (broad match).
If a broad match keyword is more expensive than phrase match? It could be that the broad match is pulling in irrelevant, yet expensive keywords as synonyms for your target term. It could be that your Quality Score and Ad Rank are so high for exact/phrase match that you get the ad discounter pulling costs down.
The first step to improving your results is mining search terms reports to see which terms make up the broad match and their respective CPCs/conversion rates.
There is so much that goes into the ad auction that's beyond the metrics Google provides that it's very difficult to understand "why" one thing happens one way and another happens another way.
You also need to factor in search volume. You might be willing to pay all the money in the world, but if people don't type your exact match keyword in the query box on Google, then it doesn't make Google any money. So prices of clicks are not always the best KPI to measure success.
Generally, I focus more on moving the ROI of a keyword portfolio than stressing over individual terms.
Learn more about keyword match types in our lesson titled 'Keyword Match Types' from our Google Ads Mastery Course.