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On the way to discover frustrated magnetic materials that realize unconventional phases of matter such as spin liquids, recent attention has been devoted to triangular-lattice materials comprising lanthanoid atoms. Here we report our detailed study of two such rare-earth-based compounds K₂CsYb(PO₄)₂ and K₂CsEr(PO₄)₂, where the magnetic ions form equilateral triangular lattices and where site mixing/distortion effects are absent. In spite of the limited size of the single crystals that we could obtain, we conducted detailed thermo-magnetic and inelastic neutron scattering (INS) studies unravelling the spin dynamics and crystal electric field effects in these systems. Our results indicate that exchange interactions are weak and magnetic excitations essentially accounted for by weakly coupled paramagnetic anisotropic effective spin degrees of freedom. We hope our research will benefit future efforts in this exciting line of research.