Lake Como vs more time elsewhere?

You have too many places on your plate. First of all I would stay one extra night in Florence and visit Siena from Florence (75 min by bus), to save one hotel change.
In any case the ideal for me is:
Venice 3 nights
Florence 3 nights (4 nights gives you a chance to have a day trip)
Rome 4 nights
Sorrento and Amalfi Coast area 4 nights

I don’t care for Milan so I like to cut it down to zero nights, but if you need to see the last supper and a few more things you need to spend at least one night. In your case I would probably borrow one night from Milan to give it to lake Como or somewhere else.

Of course everyone is different, and I like at least 3 nights in any one place if possible.
We did stay in Venice for only 2 nights, and felt positively cheated! So much wandering to do, not to mention cruising the nearby islands.
If it were me, I'd fly into Venice and out of Rome, 3-4 nights Venice, train for 4 nights Florence, rent a car, then 4 nights Siena/Tuscany, skip Amalfi for now, return the car in Rome, and 3-4 nights there before flying home.
But it's YOUR trip! So you get to choose whether you want to change accommodations and travel and pack/unpack (carry on only!!! is a must) 7 times in 16 days.
So much to see! Enjoy!

Considering Roberto's idea above, instead of Siena, consider driving Florence to Montepulciano for a wonderful 3-4 night taste of Tuscany, instead of a day trip. To me, yes Florence is considered Tuscany, but the smaller villages of Val D'Orcia are a great companion to Florence, which is larger and has lots to see without getting in the car. Siena (I may be wrong about this because I have not been there) is larger and more like Florence than the hilltop villages in the Montepulciano area.

JMO- but too many 1 and 2 night stays. I suspect you have used RS suggested itineraries which most of us feel are far too fast paced. A 2 night stay is just 1 full day in that location. Every time you change locations you lose at least a half day. Takes time checking out, getting to train, train trip, getting to new lodgings, checking in, getting oriented. Lather rinse repeat every other day or more is exhausting and you'll spend more time doing that than actually BEING somewhere.

Venice, Florence, Rome could all use another night or 2.
Siena to Amalfi is going take you the better part of a day- so you really only have 1 full day once you get there. AC needs more than that.

I'd save Milan and Lake Como and possibly Venice for another trip.

Do you know where you'll fly in to and out of?
In to Rome- or Florence- out of Naples or Rome?

if you arrive in Rome
Florence 4 nights- head right there on arrival
Siena 2 nights
Amalfi- 4 nights minimum which still only gives you 3 full days-where did you plan to stay Amalfi Town? or another Base?
Rome - 5 nights

Or fly into Naples out of Rome
Amalfi 5 nights- maybe spend first night in Naples
All the way to Florence next for at least 4 nights
Siena 2
Rome 4 or 5.

If you keep Venice
Fly in to Venice
Venice 3 nights
Florence 3 nights
Siena 2 nights- (or do this as a day trip and add 1 night to Florence and a night to Rome or Amalfi)
Then all the way to Amalfi for 4 nights- easier from Florence than from Siena
Rome 4 nights
Fly home from Rome

Alternatively skip Amalfi and spend more time in Tuscany if you are willing to rent a car for a few days
Venice 3
Florence 3
Get car
Tuscany hill towns 4 nights
drop car
Rome 5 nights

Do not skip Lake Como!! I recommend Hotel du Lac in Varenna and 2 nights is enough. I would agree you don't need to spend the night in Siena, a day trip is enough, use that night somewhere else. No matter how many nights you have in Rome, you won't see everything, so add your extra time to Rome. If you are looking for nature (since you mention hiking), I wouldn't spend so much time in Florence. Florence is for museums, if you ask me, and one night is enough (for me). Go as many places as you want, getting around is so easy in Italy.

I’ve been to all of your proposed locations. I would save Lake Como for another trip IF you like art and architecture because there is so much to see in Venice and Florence, and of course Rome. Roberto and others have suggested some good options that would give you time to fully enjoy all that each destination offers.

You could also skip the Amalfi Coast for more time in Tuscany, such as the suggested hill town idea.

I like Roberto's plan - I agree about skipping Milan and Lake Como for now and staying 3-4 nights in the other places. Italy is one of those countries that is at its best when it's savored and not rushed through. You will love it but don't let it be a blur. :)

Thank you all for the recommendations! After much deliberation, I've decided that this will be our "Culture" trip to Italy and Lake Como will be part of our future "Nature" trip to Italy that will include the Dolomites and Cinque Terre (those are both high on my list to visit). I have been to Italy before with family, and we did Rome, Florence (with some stops in San G. and Siena), and Venice (we drove through the Dolomites but never got out of the car).