Can't you just use the Flickr app (which is now pretty good) when you need to do heavy loading? I think that is better anyway, if you want to create sets, tags, etc.
Having simple way for easy posting of occasional snapshots to your Flickr stream is probably the main use case for the Flickr integration. I'm not sure why they intentionally limited it to 10 photos, but I don't think it's a big deal.
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A thing that actually happened to me-
My father-in-law was complaining that his computer wasn't working, the internet didn't work, etc. After walking through it with him, I figured out the problem was Mail.app on his Mac. The specific issue was that he had sent some emails with photos...turns out his outbox was trying to sending emails with over a 100 full-sized photos each, and it was bogging everything down.
I'm not saying 10 photos is the right cut-off (off the top of my head I would pick 20 or so), but they probably limit it so people don't make mistakes like this. Any more than 10-15 and I'm probably using the Flickr app because I'll likely want to put them all in a set.
OTOH there's no point in limiting a Facebook post to 50 characters, because hey they're just individual characters, not multi-MB files.
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Flickr is a very popular site for sharing photos. You can post to groups, friends and family can follow you, there are tags and EXIF's, etc. It's just a totally different thing than Dropbox. Plus Flickr now gives you 1 TB of storage for even the free accounts.