They aren't 'experiemental'

mRNA vaccines have been around for decades; the first report on their use was in 1993 (Induction of virus-specific cytotoxic T lymphocytes in vivo by liposome-entrapped mRNA). They haven’t been widely used because their advantages (rapid customizable development) were outweighed by their disadvantages (difficulty in manufacturing and distribution). Obviously, in the face of a fast-moving pandemic, their advantage in rapid development makes them very attractive and the manufacturing and distribution problems can be handled.

Where mRNA vaccines have been used is to treat cancers. That needs highly customizable, individualized, small-scale development, and needs to be safe for use in medically fragile people - ideally suited for the technique. Example from 2009: Direct Injection of Protamine-protected mRNA: Results of a Phase 1/2 Vaccination Trial in Metastatic Melanoma Patients.

This sort of use means that there’s actually a reasonable amount of reasonably long-term studies in their use. Here’s a review from 2012:

mRNA vaccines combine desirable immunological properties with an outstanding safety profile and the unmet flexibility of genetic vaccines. … Because any protein can be expressed from mRNA without the need to adjust the production process, mRNA vaccines also offer maximum flexibility with respect to development. Taken together, mRNA presents a promising vector that may well become the basis of a game-changing vaccine technology platform.

—Developing mRNA-vaccine technologies

Another review, from 2013, emphasizes their safety:

In recent years, mRNA vaccines have emerged as a safe and potent approach for the induction of cellular immune responses.

—Challenges and advances towards the rational design of mRNA vaccines

As does a more recent review, from 2019:

During the last two decades, there has been broad interest in RNA-based technologies for the development of prophylactic and therapeutic vaccines. Preclinical and clinical trials have shown that mRNA vaccines provide a safe and long-lasting immune response in animal models and humans.

—Advances in mRNA Vaccines for Infectious Diseases

So bottom line:

• these aren’t new
• there’s lots of info showing they’re safe
• the reason they weren’t widely used before had nothing to do with their safety
• they are ideally suited as the first response to a fast-moving pandemic, and not as well suited as the routine approach to an accustomed long-term situation