first of all, thanks for playing the demo
I won't argue your preferences (of course, you're totally entitled to them), so I'll just give you my point of view.
A key concept of the game is: you can start any mission at any time, but once the choice is made, you have to complete it in one go. No partial/temporary state saving of any kind. As you correctly note, this is part of the oldskool mindset (and still it's nowhere close to the challenges that gamers had to face in the good ol' times). This forces the player to always think twice, to always pay attention to every little detail, to stay constantly concentrated. It's demanding... and rewarding
Another thing to consider is the reason why phases exist. Their point is to give the player a break and to introduce a feeling of progression, which is otherwise impaired by the fact that the mission choice is totally free. But still they're part of the bigger scheme of whole missions, which obey to the logic described above. There's nothing more to phases than this.
On the other hand, if it were possible to restart from the last phase the difference between missions and phases would blur too much.
That said, please consider also that:
* missions have been designed taking into account all the elements the game is made of, including phases: this means that multi-phase missions are not automatically hard/frustating (there are multi-phase missions easier than single-phase ones and viceversa);
* although, at first, the thought of having to play again the previous phases might be discomforting, usually it's not that demanding (and can be also useful, as it allows to improve one's performance and to arrive to the next phases in better conditions): f.ex., relatively to "tougher and tougher" mission you're referring to, returning to exactly the point where you got stuck only requires about 2 minutes and a half (less than half a minute for the first phase, and about 2 minutes for the second one);
* currently the full version has 33 missions of all degrees of difficulty, so there's plenty to have fun with, even if certain missions might seem/be impossible (by the way: there are guys who managed to finish all of them - and, for some missions, they did need to resort to oldskool tools like pencil and paper
As a closing note, let me say that, more in general, BOH is not a game to be afraid of: yes, the "no pain, no gain" rule... rules (
), but the final experience is definitely pleasing thanks to the feeling of accomplishment that modern "enjoy for free" lifestyle/phylosophy cannot give.