From my practice I see that the most popular way to do SEO with a consultant or agency is to define a set of target terms and improve search position for those. The advantages of doing things this way are that it's easy to check progress and focus all available resources on reaching the goals. It's also convenient for the SEO agency because if they manage to reach the target positions (ideally reaching first page positions) then they have good case studies to present to other clients who have them same aproach to SEO.
If there is little to no competition on the terms the owner wants to rank better in search then doing ok SEO work delivers the wanted results and everyone is happy. Unfortunately there are fewer and fewer niches where reaching first page is easy. Things get a bit tough when competition is high, the competitors have better ranking and keep up their SEO efforts. For a term with 30+ well prepared competitors it's a challenge to reach first 3 pages in search results and as we all know second page in Google is the best place to hide a corpse because no one will look there. It's not really true as ranking in first 3 to 5 pages can still drive significant traffic to your website but the decrease page to page is steep.
The truth is that in some cases doing all you can within a reasonable budget (by reasonable I understand no more than it can be forcasted to obtain from reaching the target position) it's impossible to improve the position in an acceptable amount of time. Sometimes focusing on reaching such a hard goal can pay off but most of the time it doesn't make sense.
The main function of SEO is to drive organic search traffic to the site. If most of this traffic is qualified traffic and users spend minutes for average session on site and access severar URLs then the traffic will convert to more leads and ultimately sales. Starting from this point of view we can conclude that ranking well on a given search term is important because that term can drive a consistent chunk of the whole organic search traffic. But the site can rank well for a lot of lower search volume terms that summed up drive a lot more traffic than any high performance search term.
Focusing on lower volume search terms can be a very good strategy because improving the ranking for them it's easier and cheaper. The issue with this is that it takes a lot more work and research. It's easier to create content to build rank for 5-10 search terms and monitoring them than doing the same thing for 50-100 search terms. Taking into consideration the total amount of search terms the site is showing up for and from these focusing on the ones ranking well and driving traffic gives us a hawkeye view over the SEO performance of the website.
Researching a large number of lower volume search terms and improving the content to boost the ranking on most if not all of them is a challenge. There is a lot of work to do and budget to invest in creating quality content in high quantity but in the end all the efforts pay off a lot more than focusing on the VIP search term.
Another downside of this approach is that the agency is less motivated to do this because it makes for a not so easy to present case study. The main selling point changes from "we made X website rank first for Y term and we can do the same for you" to "we made the organic search traffic of X website to increase k times and we cand fo the same for you". As an unique selling point it may not seem to be so different but the problem is that when getting to checking metrics is easier to show vanity metrics for VIP search terms than overall lower volume search terms.
On the upside, if you have good SEO for lower search volume terms there are good chances to rank better for those much wanted VIP terms.