I resigned. Should I leave despite promises of reform?
Yes, yes, a thousand times yes.
Being unwilling to change to keep up with industry trends is an absolutely massive red flag. It implies that the company's management lacks the foresight to see the direction that their chosen industry is moving in. Over time the company will fail to retain employees because they, like you, are able to see the writing on the wall and will jump ship to better-managed employers. This will lead to a smaller pool of employees for this company to choose from, which means the company will have to be less picky, which means it will end up hiring lower-quality personnel, which means the company's productivity will suffer. This is effectively the beginning of a death spiral for that company.
Don't fall into the trap of believing that 13 years of employment means the company is loyal to you and by leaving you're being disloyal. They didn't keep you around for 13 years because you're a great person, they kept you around because you've done your duty and made them money. If you hadn't been doing that you'd've been out on your... ahem a long time ago.
On the flip side, a company has a duty to its employees to operate in a manner that guarantees the long-term success of that company. By ignoring industry changes, this company is violating that duty.
Their claim to change is also likely nothing more than a sop to try to keep you. Again, not because they like you, but because you make them money. Don't fall into this trap - I can almost guarantee that if you do decide to stay on, the promised changes will never be implemented.
Find a new employer and work there. If you really like your old employer that much, check back in a year to see if they've implemented the changes they promised, and if so consider talking to them about returning.
But I wouldn't hold my breath.