I agree one of the annoyances of Google is their propensity to drop a service or feature rather suddenly because it no longer suits them, for whatever reason.
That said, I do use Google Drive and Google Photos. Photos is quite convenient for client, friends and family image delivery. They can browse a gallery, share the link with others, download individual high-rez files or do a one-click batch download of the whole thing.
I upload images to Photos under the 16MP (IIRC) resolution limit and let it compress the files further. I've downloaded said compressed files and done side by side comparisons with the originals and the differences are extremely minute. Hardly perceptible.
Ko.Fe.: the option for compressed or not is in the new Photos service and not in Picassa (I assume since I'm not familiar with it), under the settings sidebar menu.
All in all, Photos is really just an online fallback option for me where I upload final edits for both storage and potential sharing/distribution. Same with Google Drive. Additional to these Google services, I use Amazon's Web Services S3 cloud storage service. This is not free, rather pay as you go based on how much you have uploaded and how much traffic you generate on their servers (uploading is always free), i.e. from downloading and how quickly you download large amounts, such as in a disaster recovery event. Anyway, I have a lot on AWS and it's about $10/month right now. IMO, AWS is probably a safer longterm online backup/storage service than Google because a lot of 3rd party websites and web services rely on AWS for their own infrastructure/storage. As far as I know, AWS does not do metadata scans of your images, or optical character and facial recognition either, like Google does. However, it's simply a storage service without a nice gallery option available. But that's probably OK because that kind of traffic would probably start costing you a bit of money every time you browse your collection (due to the server traffic it will generate).
Again, AWS for me is an online fallback to physical storage and backup.
IMO any free online service always comes with a catch. There's certainly one with Google - they analyze your images. What they do with that info, I don't really know. Will Photos be around forever? Probably not. But at least it has tools to allow you to download everything relatively easily if and when they announce they're pulling the plug.
Someone mentioned about no computer storage ever having a 20-year lifespan. I don't think that's as big a problem as some make out. The key is to keep on top of things and constantly migrate to newer, better, bigger storage options, whether it's hard drives or online services. You can't realistically expect to forget about your digitized images for 10-20 years and then recover them. It might happen, but it also might not. Google does offer a nice feature that lets you assign a 'successor' to your account should it ever go dormant for a long period of time (over 2 years?). I.e. should you pass, etc... so at least in theory, someone else close to you should be able to continue to access and/or recover your data.
As for two step authentication.... Google has a good tendency to send you warnings as soon as it detects log ins from locations outside your usual haunts. I.e. when you're in another country. My fear with activating two step is it wants to use my phone number as the secondary contact method, however, I'm on a prepaid cell service that does not roam outside my home country. I wouldn't be able to access that number at a time when I often most need to use the services in question, therefore don't want to get locked out. Just something to keep in mind. (Looking forward to the day when we can each have a global phone number without any roaming BS, etc.)