Is a cap a must?

The UL 1777 listing requires a rain cap. It does not have to be the one offered by the liner mfr. However, if you make a custom one, you must follow NFPA 211.

Water is the #1 enemy of masonry, esp. chimneys. It breaks down the mortar, softens the brick, stone or terra cotta. The Terra cotta tiles, if made to ASTM C-315, which many are not, does have a vitreous inner and outer face that is water resistant. However, the 1" thick ends are very porous, very hygroscopic clay. These very vulnerable ends are bedded in ordinary Portlance cement (OPC)-based mortar. This mortar absorbs more water than old lime mortar but unlike lime, does not facilitate drying. This, moisture gets trapped in the flue joints. Vapor diffusion drives it inwards towards the drier interior where it encounters the outer face of the flue tile and finding no bridge but instead a capillary break so it condenses and, by gravity, drains down into the lower parts of the chimney where it can take decades to manifest the damage. As you burn, acidic flue gases condense on the walls of the flue, thus resulting in liquid acid draining down into those vulnerable OPC mortar joints. Basic chemistry: acid + base > salt + water. The mortar is converted into sand and salt. Rain keeps these acids and salts soluble so they can migrate. The salt is drawn by osmosis to the exterior face of the chimney where it concentrates as efflorescence. Salt attracts water so an insidious cycle of water, acid and salt conspire to convert the chimney mortar into sand and salt. Thus, you are ledt with a stack of bricks sitting on salty dirt. The 'mortar' has lost its bond so the masonry is no longer intact. It will eventually become unstable and fail.

That is why you keep water out of masonry.