Why is the freshly applied paint coming off on the roller

If you select boards with knots, there is a good chance that they will bleed through, even if you use a sealer or shellac based primer. The resins in knots is persistent.

Clear boards are usually used for moldings, including baseboards. You could also use MDF (medium density fiberboard) or solid vinyl composite molding. When painted, they are hard to distinguish from wood in most applications. (I think they look a little too smooth and I prefer wood). For painted applications, there is also fingerjoint molding, which is made of interlocked short pieces and is cheaper than clear boards. Much pre-primed molding is fingerjoint. Occasionally these joints may show if the quality is not high.

For wood or MDF, a light sanding with 120 grit paper is recommended to remove milling glaze and to give the wood a tooth to better take paint. An orbital sander is fine

Then prime and paint. Many prefer oil based primer on raw wood and MDF. Some vinyl says it can be painted directly, but I would also give it a sanding (or avoid it unless necessary, such as in outdoor uses).

Latex paint is fine for a finish coat, but it tends to look less smooth than oil (alkyd) based finishes. Adding a leveling agent like Floetrol helps, but nothing lays as smooth as a good oil based enamel.

(P.S. To me, using a really smooth straight clear board, in furniture or in molding, is appreciating and honoring the wood, the tree, nature. But to each his/her own.)

Yes, you can and should sand latex if you are painting over it. You cannot expect the next coat of paint to grip if it doesn't have a roughed surface to grip to. Painting a glossy or glazed surface is like painting glass - it has no adhesion and will lift right up.

Fresh latex is hard to sand because it hasn't cured yet. You have to wait it out. If it won't sand, it's definitely too soon to overcoat it with anything but itself. (and on that, check the cans for recoat rules). You really need to leave decent curing time between dissimilar products - especially oil over latex.

There is no such thing as paint-primer. Paint companies tell you that to take your money. Their marketing claim is based on painting surfaces which are close to ideal - that is to say, well prepared and primed, with no material variations.

By "material variations" I mean material, color, porosity, chemical differences, anything which might "print through" because the topcoat reacts differently to it. I'm not referring to physical roughness like brush stipple or high spots. The purpose of primer is to bind to the underlying surfaces no matter what they are, seal them, and make them "equal" to the topcoat, so the topcoat applies uniformly and reflects exactly the physical terrain, without visible glitches for any other reason.

Done right, you will not see where wood meets marble, an area was previously painted, or where a cat peed on bare drywall.

You also need to remove surface contaminants which would foul the primer (oil, acids) or prevent adhesion (wax, silicones, linseed oil). In machinery paint, that's the classic 2-cloth wipedown with solvent. Water is a solvent, but too many contaminants are immune to it, so you need to use a chemical solvent or strong soaps, e.g. the classic TSP. You need to get the soap residue off.

Invariably when paint fails, somebody skipped one of these steps.

Why are the oil brush strokes still visible? Is this contamination like acid which is fouling each layer? (remove it). Or is it physical irregularity/bumps (sand it down). A build primer is specifically meant to be sanded. It will leave brush stipple marks far more than a topcoat will, but it's easy to sand.