Imagine for a moment you want to be an Actor. You've worked in local theater for a few years and are looking for more work. You're even a pretty good actor.
You want to specialize/only want to work on major motion pictures or as a lead role in a TV series. Your skills as an actor are indeed "up-to-par" and there's no technical reason you couldn't work in major motion pictures or TV. You prefer not to be bothered by theater, plays, commercials, or any "bit" parts.
Do you think you could get cast in only films and lead TV roles? Probably not. You kind of have to take on more menial, less prominent roles, to prove to casting agents you can handle a role with a lot of responsibility. No one walks into a casting director's office and lands a lead role without a history of other work.
Most people want to hire someone, especially someone new to them, to complete a range of tasks as opposed to specializing in only one or two aspect of the job. This is the nature of starting out in a profession. In other words, people expect you to "pay your dues" before being elevated to a more desired position.
Using only Photoshop and Illustrator is generally a position one gets promoted to, not hired for. This is similar to how major motion picture studios don't put out open casting calls for primary roles. They offer the better roles with more responsibility to those with a proven track record. If you are searching job postings for positions seeking only Photoshop/Illustrator use, you are essentially looking at open casting calls, not specialized, targeted, position announcements.
There are positions which specialize in the use of only Photoshop - such as photo retouching - and positions which specialize in only Illustrator - such as cartography or technical product rendering. The problem will be that these types of positions hire experienced people. And those people generally handled many more varied and broad tasks while they built upon their career. Essentially, someone may work at a magazine for years, then graduate to the photo retouching position and only use Photoshop. Or they may work at a web development company as a designer and graduate to a UI designer and never have to worry about any markup.
If you are seeking targeted, specialized placement you'll need a headhunter. Because I'm not aware of any employer ever offering such positions as a "job posting". There are more people wanting the same position you are than there are jobs available. And almost every company has one to two employees already proficient in Photoshop/Illustrator who have proven their abilities and work ethic. It'll be a bit of leap for them to overlook their current talent pool to hire an outside worker. Simply being proficient in Photoshop/Illustrator is not special in itself - thousands or millions are as well.
In short, yes these types of positions are available. But you'll have to be hired by a company, for a position which may be less appealing for you, and work your way up to them. You are asking to basically "cut the line" everyone has to stand in. It's highly unlikely that will happen unless you can take advantage of nepotism to a degree.
Note regarding freelancing: It's possible to get this type of work freelancing. But customarily these types of clients are the one-off clients that have 1 project for you, want it cheap, then you never hear from them again. If you wish to circumvent that entirely, then you need to focus on art and build a name as an artist and Illustrator and not merely someone who "knows how to use Photoshop/Illustrator". Again, those proficient in the application(s) number in the thousands or millions, it's not special. Really, only a unique art style will gain a living wage as a freelancer using only Photoshop/Illustrator.