There's a couple things I think are important, about this style of tea brewing - and which might help clear up some confusion.
First is, you mention the bitterness...the tea made this way generally is bitter, it is then treated to make it drinkable. This is often done with milk and sugar, chai (of India) also has spices added, and in Russia I've read it was often drunk with sugar or jam in the mouth to doctor the flavor at the source. The strong bitterness is part of the flavor, and part of the expectation, of tea brewed this way, and weaker (ie, non-bitter) tea flavor ends up feeling bland and overpowered by the equally strong flavors of the accompaniments when one expects strong tea. The fact that one can also use very small amounts to get a weaker (ish) overall experience is also helpful for those who do not prefer quite so strong a tea.
Or to think on it another way, coffee is also generally quite bitter... it is just expected and compensated for in coffee in a way that cultures which brew tea precisely don't expect to need to for tea.
As for the problems of long brewing, they are actually accounted for in this method. Keeping tea warm is, generally, not safe, but keeping it hot is much safer... basically it needs to be kept out of the danger zone. The other problem is that tea brewed or kept hot for long periods tends to be bitter, this is not usually a problem with this method because the decoction is already fully bitter. Oversteeping is usually not a problem after, for example, boiling the tea leaves for an extended period to extract every last bit of flavor :)
Also, you definitely can put tea in the samovar (this is done in india, for fully-prepared chai). The difficulty is, it will be much more difficult to doctor the tea or alter strength or flavors, so you need to be pretty sure the strength, and preparation, etc, are generally acceptable before you rely on this. It works very well with one person or a family (etc) holding tea made exactly to taste, or with tea conforming to broadly acceptable cultural standards - like a strong, sweetened milk tea, where one would not be expecting anything else and would take it or leave it.
On the other hand, since you are clearly not looking for the strong'n'bitter tea that would be expected out of this kind of style, may I recommend puer-eh teas? They are fermented, often sold in blocks or rounds, can be cheap and/or brew an awful lot of tea from a relatively small amount, and (more importantly) really do not get bitter easily. It's common to have a potful of leaves, and brew multiple pots (by adding and pouring off hot water) over the course of a day - hours of brewing time to extract all the flavor, and from a culture that prefers light, smooth, and undoctored teas. This means valuing a tea with tolerance for both long brewing times and lots of flavor, and good storage qualities as well.
Puer'eh is often said to brew sweet, which does not mean sugary but rather non-bitter, and so that would be a good descriptor to look for when looking into which ones to buy, along with (often) a described reddish brew color. You will also likely prefer the ripe, also called aged or fermented over the raw or fresh, which can be quite harsh in flavor. It also stores quite well since when sold as compressed bricks or rounds it is compact and sturdy (especially compared to dried leaves) - it just needs to be pried at before brewing for measuring and surface area.