Instead of trying to make a one size fits all argument out of SEO, understand that rankings are a by product of multiple factors unified for a common goal.
SEO should never be an afterthought, but rather a means to produce a specific attainable goal for generating and measuring traffic to your content which can be monetized through sales, lead generation or advertising/visibility for your brand.
Rankings are Produced by the Page
Keep one thing in mind, rankings are produced by the page, so the more quality pages you have, written with specific intent around 3-5 singular, plural or synomic phrases when interlinked with other related / supporting pages is often more than enough to tip the scales in your favor.
Chronology and authority add trust and reduce the time frame for new content to scale the SERPs (search engine result pages). Those pages however, still must have the needed ingredients to stand on their own once the initial evaluation has gleaned their relevance in comparison to the rest of your site vs. your competitors.
Those whose content fits more accordingly to the guidelines of search engine algorithms will rank higher with the least effort.
Your competition is irrelevant if your contents quality and links are impeccable, authority status is the goal for your website algorithmically, but it must still be appealing for the masses or your preferred audience to “get the clicks is deserves”.
The Fallacy of Keywords
If you elect to target a series of competitive keywords, be aware that the more competitive the phrase, the more time and energy you will have to invest in acquiring it.
This is why you obviously want to allocate a portion of your energy to the top tier keywords and key phrases that yield the mother lode of traffic, yet crafting a number of secondary and tertiary terms is a solid strategy for funneling pre-qualified visitors. The argument about keywords that are too broad not being worth their salt truly depends on the industry.
Most insist that one word keywords typically attract those interested in research vs. consumers that are further along in the sales cycle who use additional descriptive modifiers to hone in on a particular GEO location, product or service.
That really depends on the industry, we know for example that hitting the top 10 for SEO (since our industry is all about placement and results) can drive 70% of the total traffic for your website on any given hour, which is why getting back to the top 10 is our #1 priority. Currently we are in the top 15, but that simply is not good enough to make a definitive statement.
A website targeting the words “real estate” or “shopping” however, may not find the effort was worth it, due to the type of people typing this in are using far too nebulous a keyword they will ultimately require some refinement and additional keywords to zero in on their ideal document / webpage.
One solid method however is to:
1) start with your on page SEO factors and internal linking first instead of trying to put lipstick on a pig and pass it off as relevance. Here is a nifty little internal linking tool we developed in house for finding the best internal link / landing pages in a site.
2) Look for ways to expedite trust and website authority and create a healthy balance of internal and external links. Here are a few references for internal link building and how to augment your site from within.
3) Constantly look for new ways to leverage the internal link dynamo / juggernaut effect your own website is capable of producing like its own superconductor (once it is charged with topical relevance).
In closing, remember rankings are by the page, if your position is low on the totem pole then (1) strengthen internal linking (2) look for authority sites for inbound links (even social bookmarks will do) and (3) create a silo of related content (5-10 pages on the topic) to create the appropriate on page indicators needed to warrant search engines awarding you with a higher position.
Manage these three steps with patience and persistence, choose a tight enough niche of semantically aligned keywords and give each page enough time to find its stride (30-90 days) and your concerns about higher rankings will have subsided as you now have a solid strategy to engage in the even that your position (for your existing content) losing its footing.