It's not necessarily spammy, but you're just not making the most of your h1 and not optimising your site properly if you do leave them the same. Ultimately, the two serve totally different functions when you remove the SEO element.
Your h1 is to let people know what your page is about when they're already on the site - often, the h1 and the link in your menu is the same which helps build continuity and ensure that people get to the content they're looking for (although there may be slight differences).
Your meta title lets people know what that page is about _before _they get to your site - it's important that you provide them with more information about who you are and why they should go to your page over the other results on there. For example, if you are a leather clothing boutique in London, your h1 may be Leather Trousers. But your searcher is looking for a physical location and wants to try before they buy.... your page appears on a load of search results where people are saying things like Leather Trousers | Ethical British Leather | London (or similar - and that example is too long but you get my drift) and your result simply says 'Leather Trousers' - who do you think gets the click?
Now, when you add the SEO element back in, by not optimising your meta title you're just squandering the opportunity to let search engines know more about your page and your business. Since good SEO consists of lots of building blocks rather than one big thing, those squandered opportunities quickly add up.
