Ask HN: General hosted solution for server logs/monitoring/analytics/errors?

I've been trying to find a good hosted general solution for my company's server logs. Either my google-fu is failing me, or this is a surprisingly untapped market, or both.

Some features I'm looking for:

- Easily pipe arbitrary logs into the service

- Analyze common log formats, make them searchable/create analytics out of them

- Bonus points for nginx log analytics

- Traffic/hit rates/error rates visualizations over long periods of time.

- Big bonus points for sentry-like error

Here's some apps I tried:

- Cloudwatch (https://aws.amazon.com/cloudwatch/). I'm on an AWS stack but I really not a fan of it.

- Papertrail (https://papertrailapp.com/). Great for system logs but not much else.

- Currently trying Server Density (https://www.serverdensity.com/). Liking it a lot, but seems to be very centered around monitoring rather than general-purpose.

- Huge fan of Sentry (https://getsentry.com/welcome/). Will likely be using it regardless.

- Piwik supports log analytics (https://piwik.org/log-analytics/) but the hosted version is very pricy

What I'm basically looking for is a hosted version of papertrail+sentry+SD+piwik. Does this really not exist or am I completely missing something?