Sure you can make 7 or even 8 figures doing web design.
I personally made 6 figures the summer after I "learned web design" during one of my college school years. By then it was the early 2010s, all I did was pick up the phone, cold call less than 200 law offices with the most rudimentary proposal, not even a website or a portfolio, but I came off as uniquely passionate and those 200 calls led to about ~8 sales appointments. I think 2 of them were basically no shows but every other one was a yes except for one of them who harshly rejected me. Then I made them simple WP theme websites that looked pretty cool, and then after doing a pretty solid delivery, I upsold them on blog post monthly subscriptions that were $5k per month, SMM, and email autoresponder setup with ebook lead magnets.
This was not any harder than it would have been had I taken a job that summer, and don't give me that "cold calling is dead." Yeah right, maybe it's down 30% or something, but people said the same thing at the time and that's just an excuse. Human to human communication is never going away and ~40% of people will still pick up the phone. Also, they ALL pick up their business line. Consumer telemarketing might be dead due to all the scams but B2B calls are still fire, especially these days when you can have them look you up while you're on the call if they're skeptical.
Be the one guy who picks up the phone and makes 200 sales calls a day... every business owner knows how tough that is and how rare it is to come across the real entrepreneur who's willing to do that on his own initiative. Business owners will hear you out way more than you think because they'll respect your hustle, be able to immediately sense what level you're actually on inside, and want to go along with you on the journey to greatness.
You're not going to tell me you won't get a couple deals if you 1) do that every day until you're booked out 2) you use actually research-driven, proven sales approaches at every possible touchpoint and 3) have a clear brand and purpose laid out from the beginning and 4) actually have something good to offer that's the exact opposite of the sketchy half-baked novice garbage most people try to hawk (sounds like you do since you are talking about actually having skills as a designer first not just "what's the best get rich quick side hustle!?" like your competition these days).
Hell if you wanted to keep your job as a basic saleman for an agency you would be expected to close a minimum quota of $75k per month in business working your laid back 40 hour shift. You're going to tell me you can't handle that when it's your own business, you're keeping all the profits which are over 50%, you can build up to scaling massively, and you're building equity every month you're going along? Really? Come on man!
To give you an example, I used to be on the advisory board of a local professional organization with about 150 members and an annual budget of only about $1 million. They spent $175k to pay a local freelance designer to build a relatively simple but BEAUTIFUL ~10 page website. So don't give me the "I don't know bro, the $75k per month is impossible to hit for x, y, and z excuses." No it's not, you just need to actually be a little serious and have your activity aligned with what you do: if you want to just be a designer you can actually still make 6 figures a month doing that BUT you still have to be a hustler and in that case you'll also need a relatively rare gift for design. You'll get to that skill level pretty quick if the actual goal of every project you take is to make the best website ever... then you're going to continuously optimize along those lines. But it's going to be way easier, surer, and quicker to get to the $100k per month mark if you're the salesman, partnership creator, and entrepreneur.
If you don't understand this you probably shouldn't be in business: you'll get to 7 or 8 figures in web design in exactly the same way you would get there in manufacturing, landscaping, construction, you name it. You're going to hustle clients, outsource to scale production, develop sustainable bases of differentiation, reinvest earnings to get a huge leg up on the masses of your competitors that are out for a quick buck, research the hell out of your product, gather very detailed intelligence about your competitors etc. The money is in the SELLING and marketing, which includes the product, but not the work itself.
It's also how you slice it, some people could consider let's say Elegant Themes or even nearly any SaaS company, even AirBnB, as web design companies way back when they first got started. What they did is, as they went along, they started diving deeper into a specific idea and then scaling that out in a unique way.
What they did was they were smart, formed partnerships, seized opportunities, took risks.
In this way you can make 10 figures a year in literally any field. I'm not saying there's anything close to a guaranteed path to that level, but there is for sure a guaranteed path to 8 figures a year by taking action over a long sustained period, hustling hard, talking to a ridiculous amount of people, using your brain a little, outsourcing the actual production, indefinitely reinvesting the profits back into your sales funnel, etc. That's actually really hard in terms of the amount of work and sacrifices in your personal life and it's not for most people, including myself. But it will always work unless something crazy happens.
On a lower, shorter-term level, 7 figs a year is 100% guaranteed in my experience if you just hustle clients and outsource without even innovating or doing much reinvestment. Hell I know a salesman who makes a 10% commission for selling digital agency services who thinks he's a baller because he makes over $100k a per month and talks up how he sells 7 figures a month. The guy he works for probably makes 3 times what he does every time he makes a sale.
You're starting a web design agency so no excuse to not do the same thing. Sales pipelines, TALK TO A LOT OF PEOPLE WHO WON'T FLINCH AT PAYING A 10X PREMIUM FOR A JOB WELL DONE, and hustle.