You can’t resist the tide of history. If the technology exists to increase convenience, cut through red tape, etc, and you choose not to make it available to the public, the next guy will, and then he’ll just be the one to reap the profits instead of you.
The government can try to stop these innovations, but then people will just circumvent the government (see unstoppable pirate download sites for an example of that).
Convenience for whom?
Let's step back and ask ourselves who the "customer" is in these securities markets. The original purpose of issuing publicly traded shares of stock was for a company to raise money for capital to expand, invest in new opportunities, replace capital equipment, etc. Over the years, stock trading has effectively replaced the company owner with the investor as the "customer" in most trades. Making it more convenient to do this has simply accelerated the process and placed more intermediaries between the company's management and the owners/investors.
Have you noticed that GameStop's management and its business prospects haven't even come up in any of the conversations and media reports about the events of the last few days? This isn't even about GameStop anymore; it's about speculators playing games with its shares.
Interestingly, this is one of the reasons why someone like Donald Trump apparently never liked the idea of going public with his companies. As far as I can tell, his companies were all organized as sole proprietorships or limited partnerships. This limited his options for growth, but it protected him from the uncertainty that comes with losing control of the ownership of your own company.