Identical H1 tags on multiple pages occur frequently. This is because CMS systems such as WordPress are often used with design templates. Many of these templates define the logo in the menu as H1. As a result, the H1 is identical on all pages.
Even independently of this, it is of course possible to use identical H1 tags on multiple pages. However, the question is, is there an advantage in doing so? If there are actually several pages for one main keyword, there is a risk of keyword cannibalisation. Using identical and actually matching H1 tags on multiple pages is therefore most likely the result of a problematic keyword strategy.
You should not use unsuitable H1 tags in the first place. A recommendable use on multiple pages does not seem very likely, at least apart from the logo design question. So the answer is: You can, but you probably shouldn’t.
A missing H1 heading is a missed opportunity because a H1 has a clear symbolic power for Google and other search engines. It clearly indicates what your website is about and what the main topic of the page is. It also supports the ranking of the website for keywords. Not using a H1 can have a negative effect on the rankings of the most important keywords, because an important indication is missing.
However, a missing H1 is not a big deal to users. Users are not bothered by the lack of a corresponding label and instead are usually only interested in the headline, which has been visually distinguished as a headline.
And search engines? They are now more advanced in their development. The keywords in the H1 are only one of the thousands of ranking factors. Anyone who still assumes that they decide the fate of a website is underestimating the complexity of content analysis.
Empty H1 usually have a very simple reason: On templates for CMSs like WordPress or Joomla the logo is often marked as H1. If there is only an image and no text here, the H1 is “empty”. In principle, however, this is not a serious problem, since it is quite possible to use more than one H1, the most important heading on the page can also be marked as H1.
Having more than one H1 heading on a page is not allowed by the HTML5.1 definition, but negative consequences are unlikely. For a long time, the rule was that there should never be more than one H1. John Muller, Google’s Senior Webmaster Trends Analyst and a key speaker for the company, pointed out in a Google Webmaster Hangout back in 2017 that contrary to popular belief, this was not a problem.
He said it was normal for there to be different areas on a website (the popular one-pagers are a good example of this), which can of course be marked with their own H1. The “only one H1 per page” rule persists, but it is outdated. If the division makes sense, multiple H1s have no negative consequences.