"Home server compatible" routers would be nice. Devices could request opening a port, and you verify the action on the router GUI. Then some dynamic DNS server assigns you a nice name.
I think the desire is definitely not there to make things this easy to use - precisely because of the Cloud-Zeitgeist that we're all involved in ..
I wouldn't save my photos on a platform that changes every few months (Google Photos/Plus/Drive), might be gone in two or three years, analyses images, builds face databases, and keeps your pictures ready for the NSA to access, for any purpose other than sharing images with other people.
ASUS RT-N56U. Got one at home. It can update dynamic DNS for you (most unbranded routers can), but then goes on to add a USB port and a few "apps." One of them is a file storage host, and even file syncing (DropBox-like) app that runs from your own home.
Learn to say no to the equipment that your ISP offers you, the reason it's "free" is because it's trash.
I'd suggest an OpenWrt compatible router. It's actually free (open source) :)
Great support for dynamic DNS too (obviously, it's just Linux): http://wiki.openwrt.org/doc/howto/ddns.client
And it turned out the thing I was describing (easy port forwarding for home servers) exists and is also supported by OpenWrt: http://en.wikipedia.org/wiki/NAT_Port_Mapping_Protocol