Another luggage question

The foreign carriers are pretty much unified on the 55 cm (21.5 in) limit. Remember that line from Dirty Harry, "You gotta ask yourself, 'Do I feel lucky? Well, do you?'" Some years ago I downsized all my luggage to European sizes, rather than the size accepted on U.S. carriers.

Edited to add: Yep, that includes the wheels.

You have to check their luggage size box before you board.

Your real problem may be the 8kg weight limit.

**From Alitalia website:
https://www.alitalia.com/en_us/fly-alitalia/baggage/hand-baggage.html
HAND BAGGAGE
YOU ARE ALLOWED ONE ITEM OF HAND BAGGAGE WEIGHING NO MORE THAN 8 KG AND MEASURING NO MORE THAN:

55 cm HIGH
35 cm WIDE
25 cm DEEP
SIZE AND WEIGHT
The hand baggage you bring on board with you may weigh no more than 8 kg and measure no more than 55 cm in height, 35 cm in width and 25 cm in depth including handles, side pockets and wheels.
Alitalia also lets you bring an accessory of your choice from the following:

Briefcase
Laptop computer
Handbag/Small Purse
Small Backpack

Before proceeding to the boarding gate, check the size and weight of your hand baggage with Alitalia ground personnel or by placing it in one of the baggage measurers near the check-in desk. The hand baggage of passengers who fail to perform this check may not be accepted on board.**

The amount extra you could getting a 21 inch suitcase of the same construction as a 20 inch suitcase (hard sided, soft-sided, similar wheels, etc.) is relatively small. Think an extra sweater, pair of pants, etc. If you are doing carry-on wear your coat, or have your extra shoes in your backpack rather than in your carry-on, bring only minimum toiletries and pick up some new things to try in Italy.... Plan to do laundry a bit more often...

If you plan to ride trains and buses while in Italy, the smaller the better. If you can get away with a 19 inch carry-on, go for it. Just keep in mind, Italian grocery and department stores carry pretty much anything that can't find room in a suitcase...

Also do these bag sizes include the wheels?

When the airline is measuring it, it includes EVERYTHING, wheels, handles etc

When the luggage manufacturer gives a dimension you need to check the fine print to see what they are including ( and best practice is to take a tape measure to the store and measure it yourself)

Are they lenient on board?

If you are in coach, I would not expect any mercy. If in biz or 1st, they may be a bit nicer.

Can anyone recommend a specific bag ( with 4 wheels) that they actually took to Italy with these dimensions? I appreciate the above feedback and will adhere to the guidelines.
Thanks you all are so helpful. I have already earned so much from reading this forum on italy!

Remember that line from Dirty Harry, "You gotta ask yourself, 'Do I
feel lucky? Well, do you?'"

A man has to know his limitations.....

Why a spinner?
You lose 2" of storage space - if you had a 2-wheeler the wheels only project down, below the bag, a little bit.

Good for you for thinking through everything now. Get one good 'small' (fits the airline restrictions) bag that will be good for subsequent trips on other airlines.

P.S. I don't own a spinner and can't recommend one. I'm happy w/ the Rick Steves 2-wheeler.

wbfey1 Hahaha love it Dirty Harry

Evan the reason is that it was a suggestion from my Aunt who just traveled there. I am not sure it is the best, but I think it may be.
I am disabled, my leg, so I have limited walking etc.
She liked this style and thought it would be easier to drag.
Here is the scenerio; My Hubby and I are going to pack light. I am going to purchase a 19" bag with wheels and he is going to have a 25-27 inch bag to pull and to check in. I have decided that I do need to bring my walker with wheels. I plan to set my bag on it and push it at some times. We each have a travel safe type crossbody bag to bring on the plane.
We need one big suitcase bag because I need to bring a backup body part....
(I hope you are laughing but it is true!) I have a prosthetic leg.
I carefully and obsessively read many of the posts here to make good decisions. We are tough and can hack some of the cobblestones etc. I chose northern Italian towns so the terrain is flatter. We have an apartment(s) so we can chill when I get tired.
We are keeping all site seeing expectations low just in case I have a physical problem. We are just to happy to go to Beautiful Italy, see sights, smile at people, have coffee, smell the smells and just "be there."

The larger wheels on two wheel bags roll better over uneven surfaces. To get really good wheels on a spinner, I imagine you have to get into a fairly pricey model.