You can have more than one H1.

Where the rule came from

In early HTML the H1 was effectively the document title, and there was one document, so there was one H1. It was a sensible convention. HTML5 then introduced sectioning elements and an outline model in which each section could reasonably carry its own top-level heading, and the strict single-H1 reading stopped matching how pages were actually built.

What kept the rule alive is that it is trivially checkable. A crawler can count H1 elements in microseconds and produce a red row, which makes it excellent audit filler and gives it the appearance of a standard. That is the same reason keyword density and word count survive: a number that is cheap to compute gets treated as a number that means something.

The heading faults that do matter

Headings chosen for how they look. Marking text as H3 because H3 is the right size, or dropping to a styled div because H2 is too big, destroys the structure while leaving the page looking correct. This is the single most common heading problem in real templates, and no H1 counter catches it.

Headings that say nothing. "Introduction", "Our approach", "Why choose us" describe the shape of a document rather than its content. A heading is a summary of the section under it, and one that could sit above any section on any site is not doing that job. It also makes the passage harder to lift, which now costs you on the extraction side as well.

No headings at all. Far more damaging than having two H1s, and much more common than people expect on commercial pages, where a wall of copy sits under a hero with no structure beneath it.

A skipped or scrambled hierarchy. Jumping H2 to H4 and back, or ordering headings by visual weight rather than by nesting. Google will cope. A screen reader user navigating by heading level will not, which is the part of this worth taking seriously.

The real reason to get headings right

Accessibility, not ranking. Screen reader users navigate long pages by jumping between headings, and a correct hierarchy is the difference between skimming a page and reading it linearly from the top. That is a genuine user need with a legal dimension in many contexts, and it happens to produce exactly the clear structure search engines want anyway.

Which is the useful way round to think about it. Build the heading structure for the person using assistive technology, and the SEO version comes free. Build it to satisfy an H1 counter and you can pass the audit with a page nobody can navigate.

So what should you actually do

In practice, one H1 per page is still a reasonable default, because most pages have one subject and saying so once is clear. Keep it if you have it. The point is not that you should go and add more H1s; it is that finding two is not a defect worth a ticket, and a template producing two for a good structural reason does not need rewriting.

Spend the attention instead on whether the headings describe the content, whether the hierarchy nests honestly, and whether anyone using a keyboard and a screen reader could move through the page. Those are on-page decisions that change how a page is understood. The count is not.