Frenzen I commuted for 28 years in Colorado Springs. My main routes were 8.6 to 9.2 miles with one 6.8 mile option. My average speed was 13.5 mph on my faster, lighter bike, and 11.5 on my heavier bike with the other bike falling in between at about 12.5 mph. My average ride times were in the 40-50 minute range.
While the time in motion decreased slightly on the faster bike, the main factor in overall time was traffic and traffic lights. During rush hour, crossing major streets took time, either waiting for traffic lights, or waiting for safe breaks in traffic. On those occasions when I decided to really push it I could achieve an average speed of 14.5 mph. This would get me to the office or home about 5 minutes sooner, but I would be spent.
In the winter I rode with studded snow tires, sometimes averaging as slow as 9 mph in fresh snow and ice. In those cases it might take 55-minutes to an hour and if there was more than 3-inches of snow my speed would drop even more and it might take 75-90 minutes to get home.
Besides traffic and traffic lights, and weather, the other big factor limiting speed on my commutes was the factor of "not out-riding my brakes"...that is, not riding faster than I could brake or react to traffic and other elements of the route. Along some stretches there'd be numerous side streets with limited visibility due to high fences and such and where experience taught me cars often come flying into the roadway coming to a sudden stop across the bike lane (if there was one) or just ignoring their stop sign altogether. Even when visibility was good, and even though I have daytime flashers and hi-vis clothing, some drivers seem to judge the situation with their "lizard brain" and figure their larger and more powerful mode of transportation gives them the right of way.
Also, tight, turns, curbs, sand or dirt on the roadway, broken pavement and non-paved sections also limit speed.
I think the only ways to really make meaningful travel-time improvements over 9 miles are e-assist and careful route management. The e-bike advantage of course would boost your average speed so much that even with the usual traffic impediments, you'd notice an overall ride-time improvement.
As bike infrastructure and traffic patterns kept changing over almost 30 years, I was always experimenting with different routes and variations. Besides looking for safer options, I also looked for routes with fewer traffic lights and fewer side streets where I could maintain speed over longer stretches.
I found one for the last few years of my commuting. It was 10.5 miles...almost 2-miles longer than the average lengths of my routes, but it had fewer lights, more right-of ways and incorporated a paved bike path away from traffic. While my overall average speed was only .5 mph faster, I got home in the same amount of time as my shorter routes. I kept trying to shorten that route, but each shortcut put me back on surface streets in traffic and adding time.
There are three other factors that help lower average speeds. Tires, position and gearing.
I have found that light, supple, smooth street tires help speed things up. Knobbies and tread will slow you down. On my MTB-based commuter I have big 26x1.85 smoothies which are faster than the thinner smooth street tires I tried.
When riding upright, your upper body catches a lit of air. On my MTB-based commuter I put the bars forward and eventually added inboard bar-ends plus an aero bar. I did this to give me more hand positions as my hands got "crampy" in my 40s. But the speed gains were noticeable. Stretched out forward on the aero bars was good for a full 1 mph speed increase. However I didn't have brake levers out there. Two years ago I converted it to drop bars like my other bikes, which is better on my hands.
I also found taller gearing works better for me. I've always been a bit of a "masher"...that is a slower cadence rider, more so when I was younger. When I replaced my hybrid with mountain bike back in 1997 my cruising speed on long slight downhills dropped from 21 mph to 14 mph. I was "spinning out"...I couldn't pedal any faster, nor did I want to. I put a larger "big" ring on the triple up front (the bike is 3x7) and solved that problem while retaining the lower gears I need for hills. And just last year, I bought a 20-inch folding bike and found the top-end lacking. I added taller gearing and my average speed is now in line with the dedicated commuter bike.
One other thought. When I was 48 I was off the bike for a year due to a non-cycling injury. Getting back in shape was tough and painful and slow. Based on some discussions I read here on BF I began listening to spoken-word podcasts in one ear at a reasonable volume. I found I could hear traffic just fine (I also use a glasses-mounted mirror) and if the podcast was interesting, I didn't care if I spent an extra 5-10 minutes on a commute, or and extra 30-minutes in the case of deep snow and ice.
Those are my thoughts.
In my experience, even a slow, frustrating bike commute, even one with a flat or other mechanical issues, is still more enjoyable than driving..."your mileage may vary".
Good luck and ride safely.