According to the Efficient-market-hypothesis, you are right: the price movement of today does not affect the price movements of yesterday. However, this hypothesis describes an abstract assumption, which can be very useful for macroeconomic modeling but should not be considered as a comprehensive description of reality (The same applies to other economic assumptions, like that of the Homo economicus for example.).
In fact, there is a lot of criticism regarding the efficient market hypothesis. The Cryptocurrency-Bubbles and the Dot-com bubble are most probably the best examples that price movements in financial markets are not pure random walks in many cases, but interfere with behavioral psychological effects.
From my experience, I can assure you that many indicators are quite consistent: if you're trading in a growing market, the probability of an increase in prices is slightly higher than that of a decline (even though there will be a tipping point sooner or later). In addition, there are other indicators, such as volatility, which are relatively stable. Of course, you could try to manually determine all these indicators and include them as features in an ordinary DNN, but in practice, using an LSTM usually turns out to be easier and more accurate.