Different ADCs have different strengths. Vayne is a strong duelist, Kog'maw is a tank-killer, Caitlyn has range and a strong laning phase, Corki has mixed damage with a strong mid game, Ezreal has poke, and Ashe has utility.
Ashe's early game is weak, but her late game is quite strong. While she is immobile and lacks burst damage she has more utility, range, and innate attack speed than most other ADCs while helps her survive to deal consistent DPS. She can engage fights safely, consistently slow entire teams, and safely scout the map or get vision in jungle fights without exposing herself to danger.
Ashe's damage is comparable to most other ADC's lategame since they rely on autoattacks to deal the majority of their damage at that point. She might have less burst damage than many ADCs, but her utility can make up for it when used properly.
Jinx has less utility than Ashe since her snares have a delay and her slow is telegraphed. While Jinx may have higher DPS when her Q can hit multiple targets or she can benefit from her attack speed steroid, she also has very low innate attack speed and has to choose between her steroids; if she uses her rockets, she has abysmal attack speed and if she uses her attack speed, she has low range.
Part of the reason Ashe is considered weak is that she needs allies to peel for her a bit more than more mobile ADCs (which requires coordination not found at lower tiers of play), she has a weak laning phase (when many soloqueue games are decided by snowballing), and has trouble with champions diving her (when Vi, Jarvan, and Lee Sin were very popular).
She's not the best choice for every game as she can be a bit niche, but don't mistake that for Ashe being weak.