Some game systems have this internal conflict built into them – either deliberately or accidentally – and that's just part of the nature of the game.
Not all games suffer this conflict
In some games character death is a deliberate feature, and the rest of the system is more-or-less mindfully designed to accommodate character death as a real risk while not taking the player out of the game when it happens. These systems don't have this internal tension between keeping risks real and keeping the player in the game, because one doesn't lead to the other.
For an example of this, old-school D&D games often have chargen that's quick enough to be done on-demand during a session, and most players have a stable of PCs and followers to continue playing with immediately, sometimes already present in the party.
(However, old-school D&D demonstrates one way that such games are imperfect designs in other parts of the rules: it fails to support plot-centric play, while sort of pretending that it does plot-centric play just fine. It can, but you have to ignore or alter a bunch of rules before old-school D&D does it well.)
Why some games do suffer this conflict
In other games, character death is something that is in conflict with the rest of the design. Either it was included because "of course" the risk of death is part of a roleplaying game; or it was a hold-over from a previous edition with a design that accommodated character death better; or the designers were aiming at a demographic who have piles of disposable time and don't acutely mind downtime during play; or maybe they just didn't really inspect the reason for including character death.
In such systems, character death can often be experienced by an given play group as a misfeature – the rest of the system is off supporting a plot-centric game that is heavy on character development in complete denial that all that could be taken away (and not quickly replaced) with the roll of a fatal die.
(The worst examples of such games – where not just some but most play groups experience character death rules as a misfeature – are what Ron Edwards calls "incoherent" designs: game designs in which different parts of the rules are in conflict over what the point is of playing the game in the first place. This is one thing I think he got right, no matter what you think about the rest of his RPG theory.)
There's no easy solution that is applicable to every game, because different systems place a different role and importance on the presence (or lack) of character death. For the purpose of this question we can limit ourselves to just games that have an inherent conflict between keeping character death as a risk and getting to play as close to 100% of the time.
In a game that makes character death a risk, but it's in conflict with playing the damned game the way your group wants to, you have three options, in decreasing order of palatability:
- Jettison character death as a real risk.
- Lightly or heavily house-rule every single subsystem that makes it hard or annoying to get back into the game quickly.
- Jettison the game itself and find one that is coherent with the group's play objectives.
Unsurprisingly, most groups playing a game with that internal tension opt for (1) and make resurrection cheap and easily available, or something like that. Option (2) can take a huge amount of work, and might interfere with the reason the group uses that system in the first place, while (3) is usually unwelcome because abandoning a system with a lot of investment is actually emotionally and motivationally harder than the massive undertaking that option (2) implies.
The easiest solution isn't necessarily the best, though. It sounds like you're hoping for an compact set of house rules or para-text play procedures that can do (2) in order to get a player quickly back into the game, because you don't like option (1). In such cases though, option (3) – choosing a new game that actually supports the mode of play the group desires while maintaining character death as a meaningful risk, is a more thorough solution. It's why so many players of RPGs have opted to write their own game so that it works the way they want it to. Fortunately, there are so many and we can benefit from their work, as often there is already a game that would suit us, if only we could find it.