Why the vast majority of app developers don't publish apk files on their home page? I want to be able to install my favorite apps without installing Google play services. Apart from apps that actually depend on these services (such as paying method), why apps developed don't publish their apk on their home page?

This is particularly relevant when installing custom ROMs (without gapps).
Publishing the APK on their home page has the following downsides I can think of:
Difficulty in Tracking
It'll be more difficult to collect detailed statistics on the audience for their apps because they won't be able to benefit from the Play Store's statistics for app downloads. Whilst developers could conceivably write in data collection functions that send data to their own databases, this is extra work that's completely unnecessary if they distribute their apps on the Play Store.
No Updates
Play Store distribution allows developers to push out updates to their apps with new features or bug fixes easily. Self-distribution of APKs locks users in with a static version of the app. Again, notifications prompting users to download an update are workable but are extra work and unjustifiable especially for individual developers and small teams.
Targeted Distribution
The Play Store allows developers to exclude certain groups of users based on geographical regions or device types that are not compatible with their app. This makes for a superior user experience and prevents plenty of frustration on the user's side since they won't even be able to view apps that won't work on their device. This also allows developers to adhere to local legislation on app distribution.