First, modems in 1987 were 300-2400 baud mostly, so there isn't going to be all the color and graphics that people remember from the BBS's in the 90s.
Second, the prompt is ripe for some tweaking to get output that's more 'realistic' or tailored to what someone might expect.
And lastly, this is just the beginning. What is going to happen 36 years from now when someone loads up the latest release of 'AI' software and says 'pretend being ChatGPT from 2023 emulating a BBS from 1987'.
Edit: I can't get the sharegpt extension to work but had some fun with this prompt:
Please simulate an ascii-based dial up BBS system as it would have appeared in 1987. Please use markdown for all of the presentation, mindful of the 80x24 terminal formatting. Use colors and ascii art to improve the aesthetics of the site. Start off by emulating the dial up modem process and somewhere in the middle simulate what happens when your little brother picks up the phone and starts pressing buttons to mess with the session. You are in complete control of the contents of the BBS, the title, colors, menus and everything else. I as the user will explore using my inputs to select options and interact with the system.