I'm sorry ... clearly, you haven't given this much thought, have you?
Let's follow your scenario to its logical (God, how liberals hate THAT word) conclusion.
You want to take money from some people, and give it to other people, right? You know - that "from each according to his ability, to each according to his need" thing. So, let's assume we do that ... we put all the money in a big pot, take out the money necessary to run the government, and just divide all the money among the people (contributors and non-contributors). Everybody makes the same ... sounds pretty equal to me.
But, let me ask a question ... where's the incentive for me to be a contributor? Why would I work when I get nothing for my efforts? Why would I work, when I could just NOT work, and get the same value? So, each year, the contributors get smarter, and eventually you have NO contributors, just takers? Where does the money come from?
But, surely, you didn't mean that, did you? You don't want to take ALL the money from the contributors - just some of it. So, we'll have contributors who have SOME money and non-contributors have have some money, but clearly, less than the contributors.
But, let me ask a question ... where's the line? Anything over a million? Two million? 500,000? What's the incentive for the contributor to work harder? Why would I work twice as hard to produce $5 million, and give $4 million away, when I could just work hard enough to get $1 million??? Where does the money come from?
So, let's be logical .... we'll just take 10% of everything you make over $1 million and give it to those who aren't contributing. Oh wait --- we can't do that, because we already take 35% of everything you make. We take it, and we use it to do all those things the government wants to do ... and, even better, we make sure the non-contributors don't have to pay any of that bill. You know, they get free education, free roads, free defense, free food, free housing.
But, apparently, 35% isn't enough ... the non-contributors want even more ... they want as much as the contributors do ... and we're right back to our first scenario. And, you already agreed THAT won't work.
Why would you hang on to a demonstrably failed system? There has NEVER been a socialist society that has been successful over the long term. Name a single socialist government (anywhere) that has ever worked ... the truth is simple ... implementation of socialist policies has crippled every society.
So, let's talk about your 'lower or middle class demands a equal share of the profits' comment - do you believe that people should be rewarded by the amount of their contribution? Is that a fair statement? If you contribute 1% to the effort, you should get 1% of the reward? That seems fair, right? That's what you are calling for, right? Sounds good -- until you look at it logically (there's that damn word again).
How much does a factory worker contribute to a product? We have a ball bearing factory - it employs 100 people. It produces 1,000,000 ball bearings a day. We sell ball bearings for $.10 each, so we can agree that the factory produces $100,000 a day in gross income. The cost of producing those million ball bearings (not including labor) is $30,000 (you know, for raw materials, machines, electricity, etc., etc.) So, there is a gross profit (before labor) of $70,000. What do you want the average income per person to be? Pick a number ... tell us what you think.
I will remind you, though ... you better leave enough to make it worthwhile for the owner to invest ... or, you won't have a job at all.
I know!!!! Let's just give the company to the government .. let them run it ... that's true socialism, right? Wonder what it would cost to have the government run it ... hmmmm. The Bureau of Labor Statistics tell us that "Employer costs for state and local government workers averaged $27.38 per hour worked for wages and salaries and $15.13 for benefits in September 2013." You'll also find that federal workers are even MORE expensive. I saw once that the cost of government oversight of a federal contract is just about 38% of the overall contract.
In short, you overvalue your contribution to the final product, and undervalue the contribution of the business owner or manager.
I strongly recommend you read Ayn Rand's book, "Atlas Shrugged" - she was an avowed socialist until she started writing a book that proved socialism is the ideal economic model. When she was done, she was a staunch capitalist. Maybe you will have the same epiphany.
But, don't believe me ... just show me a single instance of the success of a socialistic economic model .. just one. We all know the definition of insanity, don't we?