There is an argument for the policy you're advocating, but it's not a policy which solves problems for free. There aren't any policies that solve problems for free: it it were that easy...
I'm only an amateur, but I'll have a go. For a start, if mobile phone companies paid substantially more taxes (let's not quibble about whether they owe them anyway) they would have less money for their shareholders and creditors. That would mean a lot of pension funds and banks more unstable than they are now, and therefore (political reality being what it is) more likely to receive government money, either directly in the form of bailouts or indirectly in the form of higher welfare payments compensating for income losses. So the government might increase its revenue, but would also increase its liabilities. This is the infamous "trickle-down effect", not that consumer spending by the rich trickles down (that effect is negligible and inefficient), but that investment by the rich (rich institution, mostly) props up the whole system.
The government could cut free of that whole system, but only by ceasing to rely on people having money to lend to it. But for the government to stop borrowing would need an instant cut in spending to levels most people would now find intolerable; and even if a lower level of government spending were desirable, the speed of the cuts would be a serious economic shock. That is the situation that Greece, and possibly now Spain, find themselves in (involuntarily): they have got into a situation where no-one will lend to them, or rather they fear that that could happen at any moment. The dramatic consequences, mostly in the total lack of control which results, are frightening.
Of course, Greece and Spain have the added disadvantage that their currency is (forcibly) over-valued for their economies. We have the luxury of controlling our own currency, which gives us some more leeway. If we interpret the government's monetary policy charitably the Quantative Easing programme is designed to push down the value of our currency so as to make it more attractive for rich institutions to lend money to our government. That is, of course, what the government mean by "keeping interest rates low": they mean keeping interest rates low for the government so they can carry on borrowing money to fund government spending. The balancing act comes because QE not only reduces interest rates (helping government to spend more) it also raises inflation (effectively reducing consumer spending).
There is an interesting moral hazard here. The government's interest rate strategy (I know it's technically the Bank of England's strategy, but let's not be naive) is to make lending to the government more attractive. Unfortunately that makes lending to other businesses correspondingly less attractive, and thus government borrowing makes rich institutions comparatively warier of investing in growth opportunities.
If I may be allowed a digression, there is, however, one source of apparently unlimited credit, which is Chinese savers. If Western governments don't like the tyranny of the money market they can also escape it by borrowing from Bejing. (We can, I mean: the Greeks don't have a hope - Chinese investors aren't stupid.) Financially borrowing from China makes Keynesian sense, in a recession. China has lots of cash to lend, and if we assume that we can grow eventually it makes sense for us to borrow it now. But politically it seems to me to be putting ourselves into the power of some people even more worrying than the bankers, and my hunch is that we have gone down that road far enough. Better the devil you know, perhaps.
All of this maybe true (it is certainly the argument for maintaining the status quo that is put forward by politicians from all the main political parties). But it is a state of affairs that is the result of our adoption of unrestrained capitalism. There are other economic systems. Perhaps we should give one of them a try as capitalism is eating itself. As the commenter points out, the trickle down effect is miserly and it is getting worse. More and more of the world's wealth is becoming the property of fewer and fewer people and they are getting greedier and greedier. These people are far less efficient at spending their wealth than those with average and low incomes and, as economic growth is dependent on spending, the economy is becoming stagnant. We are destined to a continuation of boom and bust with the booms becoming less booming and the busts becoming longer and more hard hitting.
So, we have to ask ourselves, do we want to continue down this unjust and economically suicidal path or do we want to go through a lot of pain now whilst we sort out the mess our greed has got us into and create a fairer economics where none are extremely rich and none are extremely poor? Just saying that this is how things are and there's nothing we can do about it is a cowardly and hopeless attitude to take. It is certainly not Christlike. Jesus had a simple answer to the inequalities in the distribution of wealth in his day. He advocated that the rich give their money to the poor. Of course, he knew that the rich would be extremely unwilling to do this which is why he placed his hope on the coming kingdom of God. But the kingdom of God cannot achieve anything on its own. It is down to the citizens of the kingdom of God, with the help of its ruler, to bring about the changes Jesus desired. Personally I believe it is about time we took our citizenship seriously and started to trust in God and his crazy, beautiful, life enhancing economics rather than listening to the defeatist weasel words of the satan in the wilderness.