For many years, basically Nikon and Canon split up the "professional" market between each other. They already had this position with analog SLRs, and continued after the transition to digital. The reason is a mix of having very good cameras, a large lens setup, especially considering the more exotic/expensive lenses mostly used by professionals and most importantly, with the service organizations. At each olympics, they would have large service centers on-site, for repair and exchange. And also outside of these events, they have services networks which enable a professional to get the equipment serviced/exchanged with loaners in minimal time, which is a very obvious benefit. Which basically prevented other brands to make a huge inroads in the professional markets.
So their profits were driven by the established systems. They were milking this cash cow and consequently were late to the mirrorless game. Their recent offerings are nice, especially Canon has some very interesting lenses for their new mirrorless system, but even for those companies it takes a whole lot of time to have a remotely complete lens offering.
It might also be worth while to look beyond the 35mm format. In 2013 Olympus brought the OMD E-M1 to the market, which was possibly the first mirrorless camera, not only matching but in a few aspecs exceeding the performance of comparable DSLRs. This shows, how much Canon and Nikon are lagging behind.
I think that’s it. But it seems they are catching up very quickly now. The upcoming EOS R5 looks like a very good camera.
You nailed it on the head for the most part.
Nikon had a mirrorless camera in the J1 series, which had some very nifty features but was just an absurdly expensive system for what you got (especially since it is basically a dead end, proprietary platform.)
Canon did a bit better with their first MILCs, but they weren't amazing. At the time they were introduced Canon suffered from a lack of on-sensor Phase Detection AF, and Contrast detection systems weren't as fast as they are now.
I mean, a big issue is glass; While there are exceptions to this, you can't just re-use an existing lens design on a mirrorless without making the thing longer than it needs to be (Which looks off on a Mirrorless.) Which means that Nikon/Canon can't just release the 18-55 EFAF Mark 10 lens.
Designing proper lenses takes time and money. I mean, the first few years I had an E-mount, the pickings were slim for lenses, while the a6000 was a good start it wasn't till the A7II and A7RII with their ability to do usable PDAF with adapted lenses that the platform felt safe to pick up.
But also think about it from a marketing perspective - even now most people buying cameras aren’t professionals. A big bulky camera right next to a svelte one in a store will look dated. That said Sony went too far with it, in my opinion. A nice grip is important for professionals.
How can glass lenses be "faster?" Allow you to shoot with a faster shutterspeed?
The biggest things holding back mirrorless technology previously was battery life and autofocus technology. I am not sure why Nikon and Canon didn't invest more into mirrorless technology sooner, and I'm no photography expert, but I think they were just too entrenched in the DSLR technologies they pioneered.