Josephson junctions with non-hysteretic current-voltage characteristics form the basis of most superconducting electronic circuits including RSFQ logic and programmable Josephson voltage standards. In contrast to conventional SIS devices, Nb/Al-AlOx-Nb (SNIS) junctions with an additional comparatively thick Al interlayer and a comparatively thin barrier AlOx are intrinsically shunted at T ≥ 4.2 K . In this contribution, we provide experimental and theoretical arguments proving that this finding is mainly explained by a broad distribution of highly-conductive barrier transparencies with a significant effect from nearly ballistic modes. An additional advantage of the proposed SNIS junctions is possibility to tune the critical voltage value by modifying Nb and/or Al film thicknesses. With observations of wide Shapiro steps up to 1.25 V at 6.3 K we show that this type of Josephson junctions can be successfully used at temperatures above 4.2 K. The presence of well-developed quantized voltage features even at 7.2 K means that Nb/Al-AlOx-Nb devices can successfully operate far above the liquid helium temperature and, in principle, are compatible with two-stage cryocoolers.