I think you have the wrong idea about the meaning of those terms, “exact”, “phrase”, and “broad”. How you use those terms, particularly the context in which you use them, matter a great deal.
For the sake of clarity, let me explain what the terms mean. And then I will discuss a couple of different contexts for the use of those terms. Hopefully, this will give you a clearer picture of the meaning of those terms.
Those terms are labels that Google invented to define how their AdWords system triggers ad impressions in their Search Network. As an advertiser, you can select keywords that are defined as “broad match”, “phrase match”, or “exact match”. There are also other matching options such as “broad match modifier”, “negative broad match”, “negative phrase match”, or “negative exact match”, but I will not discuss these varients in this post. For more in depth information on AdWords keyword matching options see this link: Using keyword matching options – AdWords Help
Now to address the context in which you seem to be using these terms:
Many webmasters use the AdWords Keyword tool to gather data about specific keywords, or groups of keywords in some cases. I assume you are discussing the match type data in this context, if not, please correct me.
It is important to understand what each of those data types represents to be able to use the data properly. The exact match data is the only data that represents information for an individual keyword. The other match types represent data for an unknown number of keywords, therefore useless in analyzing individual keyword search volume.
The whole premise of your post is based on a false notion about search volume data.
You cannot target a broad match keyword in the context of SEO, that is a targeting option reserved for AdWords advertisers. The same is true for phrase match keywords. The data for those two match types includes many different keywords, and you have no way of knowing exactly how many keywords are included in that data. You would first need to identify the individual keywords included in that data and then target each and every one of them, individually.
You are indeed missing out on a lot of traffic in the long run if you ignore short head keywords. Creating a page for a long tail keyword can be nearly as costly as a page that targets short head keywords. The best strategy, in my opinion, is to use long tail keywords that include your primary head keywords within a phrase and target both simultaneously. This way you get twice the benefit for the same effort.
