Not erases it, but it is a huge part of the solution. Will a city like Seattle have traffic still? Sure, but it will be a lot better.

I know it may seem counter-intuitive ... we think that more and wider roads will solve traffic. But it's actually not true. Here's the articles with the data to show it:

In California: "Rather than increase delay for cars, the protected bike lanes on Columbus actually improved travel times in the corridor. According to city figures, the average car took about four-and-a-half minutes to go from 96th to 77th before the bike lanes were installed, and three minutes afterward—a 35 percent decrease in travel time. This was true even as total vehicle volume on the road remained pretty consistent. In simpler terms, everybody wins."
- https://www.citylab.com/solutions/2014/09/when-adding-bike-lanes-actually-reduces-traffic-delays/379623/

New York, after putting in protected bike lanes: travel
time for cars constant
or reduced in most
cases"
http://h2020-flow.eu/uploads/tx_news/FLOW_REPORT_-_Portfolio_of_Measures_v_06_web.pdf

Again, New York: "They ease congestion and speed up traffic, the agency’s analysis of GPS data from taxi cabs shows."
- https://www.fastcompany.com/3017312/do-bike-lanes-actually-speed-up-car-traffic

London. First, evidence that 'if you build it, they will bike" "Both the new so-called cycle superhighway routes have seen cyclist numbers shoot up by 60% since they were built, according to Transport for London figures."
The result? "And that’s the paradox at the heart of all this – cycling is one of the few easy wins for policymakers. Give over a small amount of road space for proper bike lanes and, as city after city has shown, more people cycle, thus freeing up space for cars and trucks. The bikes are the solution, not the problem."
- https://www.theguardian.com/environment/bike-blog/2016/oct/06/cycle-lanes-dont-cause-traffic-jams-theyre-part-of-the-solution

The great thing about data is it counteracts our intuition, which is often wrong.