No, you absolutely don't
need a car. Whether you would
like to rent a car and explore by driving around near and far, is a more personal question.... Free gondola to town (walking the whole town is easy, parking in town not so much). There is plenty to explore near town without a car, although for some trailheads a car is needed. Festivals (Film or Blues n Brews....) could crowd town/ restaraunts on weekends- Lots of options, depending on whether you want Big Adventure ( "Via Ferrata") or a short, scenic stroll from the gondola station-- a guide can be useful to prevent mixing up those extremes. FYI, some attractions advertised as "nearby" Silverton or Mesa Verde, can mean 4 or 5 hours driving roundtrip.
To minimize airport shuttle costs, car rental might be a decent value overall. To maximize experiences, you can take advantage of guided day-trips, you'll get to see more and drive less. Assuming you are flying into Montrose/Telluride, shuttles can be spendy, it's about 70 miles. The views are great, but not if you're focused on traffic.
You could avoid renting a car, and just rent a jeep for the day, drive to Ouray and Silverton, then back to Telluride over Imogene or Ophir pass (anytime after Labor Day is fair game for early-season snow, Imogene is off-limits Sat. am after Labor Day for the 17-mile Imogene Pass race).
Yep, the Million-dollar Highway sure is spectacular, but only if you are comfortable driving a narrow, twisty road above a 500-ft cliff (too narrow for guardrails). To really explore the Alpine Loop 4WD trails, you want a "real" Jeep (NOT an airport-rental psuedo-SUV). As a 4Runner owner, it pains me to write that, but what they rent is "Jeeps". Depending on your off-road driving skills, you can drive yourself, or go on a guided tour. Some Telluride-area 4wd roads are black-diamond-level driving. If you rent a jeep, they will ask your skill level and tell you what roads/trails to avoid (such as Black Bear).
The wildfire smoke is hit-or-miss, since this year wildfires aren't too bad in CO, horrible in CA/OR/WA we have been getting smoke from those. If you subscribe to OpenSnow all-access, there's a great smoke map predicted 18-hours out.
Here's a link, for any who haven't yet discovered OpenSnow's awesome ski-weather resource:
Your trusted source for the most accurate weather forecast, snow report, high-resolution weather maps, and ski conditions information.
opensnow.com