I run a similiar setup for almost 1,5 years. LineageOS 14.1 with f-droid "store"; syncing contacts and calendar with davdroid over nextcloud; also switched search to duckduckgo (on desktop, too) and I really don't miss anything. Another advantage of missing Google play services on my now 5 year old phone is, that the power last two times longer than before. A google service free phone is absolutely usable in my opinion and I can recommend this to anyone who does not want to share all its data with google. Some word to the play store problem: I've heard of so much malware and fake apps there, that I don't think the trust is less for an open source community. To install any proprietary apps, I can recommend yalp store, which uses the play store. It's interesting to see how much apps depend on google services and the only trusted source is the google play store, which requires a google account (which I don't have). At this time any request on providing google free apps are ignored or denied with google play being the only trustable source for android. I don't think that this is true, at least not for people with some technical background.