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Grandma would probably use MyMonero over the core GUI (though maybe not for longer-term storage of value). That is a good example of third party solutions starting to specialize.
By "generic" user I didn't mean grandma but a wide base of all sorts of users without specialization, and that's where MyMonero fails to hold up. That includes people who see the primary use of crypto today and for the indefinite future as a store of value, medium- to long-term speculative investment, or perhaps as a medium of exchange that is somewhere between reasonably and very private. In all of those cases many won't want to use a web wallet.
I have to disagree here. People over the age of 55 were raised on cash and in many cases are very distrustful of third party payment providers and are very fearful of identity theft. They are also very privacy conscious. Furthermore they are far more likely to adopt the technology of their grand children than the technology of their children. For a senior the strongest appeal of crypto currency is likely its cash like properties, (cash one can use on the Internet) since that is their comfort level. If they adopt a crypto currency it is highly unlikely that they will then turn it into the very thing they are trying to avoid.
As a baby boomer, my take is that the baby boomers can be a very receptive demographic for Monero, but I doubt we will buy in if we are sold the same technology we rejected 20 years ago.
I am 55 and atypical I suppose. I will tell you how I use crypto. I am mining etherium, converting to bitcoin through an exchange sending to coinbase and using my Swift card to buy cat food. Monero will need to be that simple or simpler to use. Are there plans to offer a debit card?