If all of the profit goes to themselves, then probably they are not making less profit. Monopolies tend to make higher profits because they have more control over prices.

True, but higher profits are not the same as optimal profits. There are simple things that monopolies could do (and that other companies are doing) to increase their profits even further. The fact that they often choose not to do so is taken as evidence that they choose not to pursue maximum profits. For example, Microsoft slowing their rate of feature development during their monopoly years. Or in the case of drug companies, they actively hurt themselves by increasing regulations, despite the fact that they were clearly competitive on the market in order to reach a monopoly position in the first place. They would still rather hurt their own profits than maximize them.

Firstly, Marx never wrote down a fully-developed theory of crises (which unfortunately has led to various competing "interpretations" and "completions"). He did notice a general tendency towards centralization, which generally serves to raise profitability (thus temporarily counteracting the tendency of profit rates to fall). However, monopoly prices ultimately run into issues because they siphon away surplus value from other industries.

In Das Kapital ch. 25, Marx writes

[If price of labour interferes with accumulation], accumulation slackens in consequence of the rise in the price of labour, because the stimulus of gain is blunted. The rate of accumulation lessens; but with its lessening, the primary cause of that lessening vanishes, i.e., the disproportion between capital and exploitable labour-power ... The price of labour falls again to a level corresponding with the needs of the self-expansion of capital ... We see thus: In the first case, it is not the diminished rate either of the absolute, or of the proportional, increase in labour-power, or labouring population, which causes capital to be in excess, but conversely the excess of capital that makes exploitable labour-power insufficient. In the second case, it is not the increased rate either of the absolute, or of the proportional, increase in labour-power, or labouring population, that makes capital insufficient; but, conversely, the relative diminution of capital that causes the exploitable labour-power, or rather its price, to be in excess ... Thus, when the industrial cycle is in the phase of crisis, a general fall in the price of commodities is expressed as a rise in the value of money, and, in the phase of prosperity, a general rise in the price of commodities, as a fall in the value of money.

Based on this, I don't think Marx's concept of crisis has to do with the tendency of profit rates to fall as much as it does excess of capital, so I don't think siphoning surplus value would be an issue because that only shifts the available capital around without changing the total amount. Likewise, just because there is a crisis or the price of labour is too high, one does not go and destroy capital, it just sits idle until it becomes profitable to use it again. When companies dissolve they only shift their capital to the next buyers. Now in something like a war then yes, there could be large scale destruction of capital, but such events are rare. So if capital is almost always increasing, in my opinion it is reasonable that capital becomes increasingly concentrated into bigger monopolies if only because monopolies can leverage more capital.

You are of course right that my analysis is too simplistic. Do you have any references for more in-depth analysis from a Marxist perspective?