Another thing that would be useful in selling high level adventures is redefining the "Tiers of Play", giving them names that clearly tell you what to expect, and then making likelihood of starting at higher levels more front and center.
Here's an idea. Since D&D makes so many different starter sets nowadays, how about one that that starts at like 11th level?
Players with experience are used to starting at 1st level. DMs are used to starting at 1st level. When you start at 1st level it is way less likely you'll play high level than if you start there!
The only way for this to happen is for WotC (or someone else with lots of name recognition and market share--maybe popular streamers) to make it front and center. If Critical Role started a campaign at 11th level, I bet lots of new people coming into D&D would be interested in that too. But WotC can do it in how the books are presented. First, you really do need a high-level starter set, since you can't really use a starter set without reading and absorbing most of what's in it. On the other hand, apparently a lot of people just reference the PHB+DMG, rather than reading and understanding what's in it. Both the 2014 and 2024 PHB have a sentence or two about potentially starting at higher level, but none of them put it front and center, so it makes sense that new players don't really even think of that as an option. It needs to be right there in the section about having a section zero or discussing the campaign--not in the character building chapter. There should be campaign decision steps, things like theme, etc, and one of the first and biggest ones should be campaign level. Something like this:
Step 3: Determine Campaign Level.
Every campaign starts at a certain experience level, represented how much adventuring experience, training, and raw power your characters might bring to the campaign. The DM should select a level that best fits the type of themes and settings to be explored. Starting at single-digit levels should never be assumed. From highest level to lowest level, the categories of campaigns are are described below.
Planar Champions (Levels 17+)
Characters at this level typically adventure out on the infinite planes where the sorts of threats needed to challenge them are found. They face...
World Heroes (Levels 11-16)
At this level, your characters are probably some of the best known heroes of your world. You are likely to face at least one world-endangering threat during the campaign. Your adventures might involve overthrowing or founding nations or facing ancient mythic foes. It's very unlikely that your adventures will be isolated to a particular location or region, as you'll need to range far and wide to face the sorts of challenges appropriate for these levels. You might...
Champions of the Realm (Levels 5-10)
Characters at this level are quite powerful, and usually treated with at least some degree of respect by the authorities. The kinds of adventures they participate in can include almost all of the classic D&D threats, including high level foes like dragons and liches with enough lead up. At this level, it's quite possible that your adventures might be limited to a certain nation, or centered around a city, where you face threats and problem limited to that region...
Real Adventurers (Levels 1-4)
Characters that start at these levels have learned the skills necessary to be an adventurer, but are still gaining experience with the world. They typically are only well-known in locations they've personally visited, not across a nation or region. Local authorities and petty criminals can still pose a credible threat to these adventurers...
(See what I did there by listing high level first and making the hypothetical reader go through the list before they get to low level? That's what you have to do to reverse (or in this case, just expand to offer more options) role-playing generations of tradition.)
Put that in the PHB, make a starter set at level 11 or so, have popular streamers start at high level, and people will play it.