In this paper, we consider the advantages of an alternative design concept for HTS accelerator magnets operating at 20 K or above. The idea is primarily built on using REBCO tape as the main conductor, but may be applicable to other HTS. The key concepts are to align REBCO tapes in the most favourable field orientation and to make joints for every turn such that the tapes will not have to be wound over the saddle ends. We argue that such a concept involving resistive joints is viable at 20 K or above due to an increased cryogenic efficiency, and has multiple advantages that would more than compensate for the resistive heating cost penalty. First, the favourable tape orientation can allow a much higher current carrying capability. Second, the short unit length of tapes equal to the length of the magnet will be much more economical and can be specified at a higher performance than a long continuous piece equal to the number of turns multiplied by the length of the magnet. Third, any defective conductor can be replaced easily and at a much lower cost than an entire coil. Fourth, with each tape separately sourced and connected, efficient grading with stress management can be achieved. Fifth, the straight section of the magnet would be modular and easily scalable for production in industry. Correspondingly, the most challenging part is the end cap design and joint technology, whose geometrical constraints are well within national laboratories' capabilities, making the R&D and prototyping phases much more affordable, with a turnover time much quicker than testing full size magnets. Additional attractive potentials include conductor development (e.g., double-sided extra thick REBCO), novel diagnostics (e.g., individual tape quench detection and protection), synergy with fusion devices research (e.g., demountable joints), and other possibilities.