For living in the city, an electric bicycle is absolutely perfect .. or at least here in Nashville, where there is little public transportation to lug the bikes onto.
Typical production electric bikes weigh in the 40 to 60 pound range. Definitely heavier - you will feel the extra weight if you turn off assist, and certainly if you lug the bike. But the assist more than overcomes the additional weight when riding, range / access to charging infrastructure is a non-issue, and even a small increase in speed increases safety and comfort riding in traffic.
For example, I often ride with coworkers to lunch on a conventional pedal bike. Many of the streets we ride on are 25 mph, and we can mingle with traffic relatively safely as we can hit 20 mph pedaling hard. However, there are some 35 mph connector streets without bike lanes that are honestly unsafe to ride on (but we do anyways). I feel that being able to hit 25-30 mph for short distances significantly increases safety when mingling with road traffic .. and in many cases it is not a choice between bike vs electric bike but instead car vs electric bike.