Optical media for archival purpose has the problem of a rather little capacity.
This was the reason, why the boxes with optical media and changer mechanism vanished 10 - 15 years ago…
Speed was a topic, too.
We will see if this changes in future. 
Wow 100 years. Don't think tapes would last that long. 
I feel like there isn’t much that’ll last that long. I’d think that you’d have to upgrade your media every 10-20 years at a maximum to whatever the current standard is. Even if the disk lasts 100 years, are you keeping around a drive and computer for 100 years to read that data? In 100 years, will people be able to connect it to the network? Just think if the networks we had 30 years ago? Token ring? Thicknet? Will people understand the software and interface? How much has IT changed in the past 10, 20, 30 years already. Imagine how much it will have changed over the course of 100 years. For sure, there’s no way you can just let it all sit for 100 years and expect to retrieve that data. It’s certainly not going to be a case of plug it in, turn it on and start restoring.
We have 100 year requirements for a good portion of our data.
I laugh because we have applications that are deprecated but sometimes need to keep the data still. I do my best to isolate a VM with the old OS, software and a way to view or read the data if possible.
That being said, who knows in 10,20,40,80,100 years what’s going to be out there and if much if it will be accessible. Will I be able to boot a server 2012 in VMware 25? will VMware even exist? will computers exist?
Regardless, laws are laws, so if you need to keep it, you keep it. LTO tapes are the best medium for much of this data that will never need to be accessed. Keeping multiple copies is required to prevent a tape failing or snapping. The tapes are never kept for 100 years. Every 5-10 years you end up upgrading from say lto 4, to 6, to 8, to 10 etc. Data gets copied, tapes are faster with more density and life continues.
My job is to meet the law requirements and not predict the future. When I notice things have changed, I bring it up as a CYA, and the business can decide if they want to restore one of these applications and create a project to export it all into a new modern format.
The main issue with these policies are the size that things grow to. I already have many PB’s of data to manage and keeping everything forever becomes expensive.
We already have media that can store data for centuries: PAPER 
Joking aside, we have seen such requirements , especially in financial and tax businesses as you all can imagine, there’s no easy answer to this. Probably, even more than keeping the software and its compatible hardware able to boot, we should look at some “open format” to write the data, so that even a different software in a century from now would be able to read it. Again, I think about human written language.
For the media itself, I’ve seen usually tape as already said, and they use external media transfer services to move the data from old generations of tapes to new ones.
Following along the same vein, there are a brilliant article on how to warn future generations about nuclear waste storage facilities.
At the moment, waste from nuclear plants is mostly buried, signs put up and apart from the people involved, mostly forgotten about. How do you ensure someone coming across the site in 100 years time will know they should avoid the location.
Really good read here: How to build a nuclear warning for 10,000 years’ time - BBC Future
Same with data storage, how can we ensure we are able to retrieve the data from the storage medium used to store the data on and the software needed to read it again.
Store the physical workstation together with the software? What happens if the workstation has a fault. Are parts easily available or do you but spare parts as well?
