So just still thinking about Cyrodill and gathering resources. I mean some valuable resources.

So there are farms and mines around Keeps, but why should we protect them?

What if they give us valuable resources? In case taken by enemy and taken back it needs be 24 hour period before they start to produce.

What if by taking them (from enemy) you automatically got some resources?

The guild who own farm gets bank filled with resources.

That would be some alternative to manual gathering and some reason to hardly protect farms.

Castles/Keeps get the resources from its area of buildings (farms etc)

I think, those resources are used automatically by the central keep/castle to make itself stronger with stronger NPC guards and garrisons.

just something i expect to be in game.

yes, but this is (I will try to name it) "shared resource to make keep stronger". I was thinking about personal benefits from owning farm - for example getting milk useful for provisioning.

i am pretty sure those areas have basic ingredients available from those sources that make milk etc.

if not the stuff is collectable around the area.

pretty sure you need to collect them as farms are not owned by 1 person, its owned by guild.

would you have strong engagement to protect mill if it is only used to collect few basic ingredients?

What if there are rare and valuable ones also?

If they had crafting gear resources in the pvp area and to increase my crafting lvls I might attempt to go there and sneak around and gather but if they don't then I have no reason to go to the zone.

The reasons to protect the resources around keeps (lumber mills, farms, and mines) is because they offer upgrades to the keep that they are around. Lumber mills increase the amount of life that keep doors have, mines increase the amount of life of walls and may do other things, and farms upgrade the NPCs that are within the keeps and patrol around the keep.

So it's a very smart idea to try and keep hold of these resources otherwise your keeps will become much weaker and easier for people to take control of.

Do you think to convince PvE crafters for this? Perhaps they have other sources of resources, so they will not be much interested in making keep protected.

What does this have to do with crafters? The keep resources don't just spew out free crafting materials for people to collect. If you want to find crafting materials you have to go out into the world to find it.