It is important that oil remain in the filter after shut down. Upon start up the flow of oil in the lubrication system starts at the oil pan sump, up the pick up tube, through the oil pump, and then to the filter. From the filter the oil travels directly to the main bearings. If there is no oil in the filter it will take a moment for the pump to fill the filter while meanwhile the main bearings run without oil. A filter with a bypass valve does combat this tendency. Bypass valve, not to be confused with an anti-drain back valve. A quality filter will have both. Note: The bypass valve main purpose is for the oil to bypass the filter in the event of a filter restriction.
It is especially important for a filter to have an anti-drain back valve when the filter screws "sideways" (horizontal) onto the block, since over time gravity will empty the filter. Gravity is not such a factor when a filter is mounted in a vertical position.
This is why many engine designs do have their filters mounted vertical, and remote filters are mounted vertical. Whenever I change the oil in an engine where the filter is mounted vertical, I prime the filter by pouring oil into the filter before I install it so the bearings get oil right away. Not really possible to prime the filter on my stock mounted filter 4.6, because by the time I get the filter into place, and screw it in, much of the oil will drain out in a mess. This occurs even with a filter with an anti-drain back valve because oil will spill out of the center outlet hole.
To be clear (and I've made a correction here since I originally wrote this information), when the engine is off, the spring holds the flap of the valve over the intake holes to block oil from draining back, and when oil pressure is present the flap is pushed away, and the holes open allowing oil to enter into the filter. A simple one way valve.
It is important to consider that a hot filter, mounted sideways, without an anti-drain back valve, will empty in only a few minutes or less. Or, about the time it takes you to buy a big gulp, and return.
On race cars I have built, and driven in the past. we've installed an electric pre-oiler that primes the lubrication system before every start up. We would also run this pump after shut down to cool the engine. And on turbo cars to keep the turbo from coking up. On first start up rebuilds on older engines I've used a ground off teeth oil pump driven gear to drive the oil pump with a long shank slotted screwdriver drill bit, and and electric drill run down the distributor hole. Pressure tank feed to the oil sending unit hole works better tho'.
Here's a exploded view of an Amsoil filter.