Will a Site With an Unusual (but Large) Link Profile Compete?

I'm working with a company that sells landing pages (not actually, but close enough), so it has backlinks from all the sites that use its landing pages.

99% of its backlinks have come this way. The links all have the same link text and come from many different types of sites.

I want to compete for high competition keywords because this link profile is strong, but I'm worried that the strange mishmash of link sources and the unusually consistent pattern of link text will hold it back.

I'll try either way, but do you have any insight for me going in?