This implies that the game is dangerous and maybe that life-restoration magic is hard to come by.
Not necessarily. It implies that played by-the-book, attempting a deadly encounter is likely to leave permanent casualties. There are many scenarios possible where bringing back the dead is made complicated or not possible:
A rout, where the dead are left to lie while the rest of the party flees.
Destruction of the dead character's body
Lack of funds at low level
Lack of access to a high level NPC
Lack of a good relationship with the high level NPC capable of raising the dead
However, it doesn't seem unreasonable that back in town, there's an NPC cleric in a local temple willing to cast life-restoring magic for the book cost of the material components, plus perhaps a small tithe.
That depends on a few assumptions, which can all be challenged or made more interesting:
It's a small town, in a sandbox setting. Stocking it with powerful NPCs can cause issues, especially when the PC group is low level.
An NPC cleric's church should be more than a shop. They have a religion that they are likely the personal representative for in the town. In a sandbox setting, they should have a name, personality and goals.
A "small tithe" may be appropriate for a local hero who has supported the church (or maybe is part of it)
Access to otherwise unavailable high level magic may come with some requirement - a favour for a favour, depending on NPC's goals.
Like the rest of a sandbox campaign, the previous actions of the players should influence the relationship with any meaningfully powerful NPC. If they have made some effort to ingratiate themselves with the church, then they may get some of the NPC's time. If they start to treat a temple like a miracles shop, they are likely to get turned away, or be asked for a better return of favour.
If the PCs (and especially the PC needing to be resurrected) have performed deeds that are questionable to the NPC or their religion, then this may prevent access
An NPC cleric faced with a decision on whether to raise someone that to them is a stranger has some spells that they can use to decide if it is in their interest (regardless of money) - Speak With Dead, Augury, Divination, Zone of Truth.
This is all a roleplaying opportunity too, that will add depth to the campaign.
My question is this, how does access or lack of access to life-restoration magic in a westmarchian game affect the game?
I don't think a "westmarchian game" requires a specific level of access to raise dead, as it has multiple traits that make it a success. I'd still call a game with other westmarchian traits, but an automatic re-spawn including all equipment as "westmarchian", if it was e.g. generally a sandbox with a gradient of challenges based on something that the players can understand, and players control timing/goals of sessions etc.
I can understand why some people would say such a game was "not westmarchian". However, there is no West Marches official brand or police. I would say that if it is easier for you to say "this is a westmarchian campaign, with access to Raise Dead in the town temple (because we assume you are all local heroes and supported by the church)", and that communicates well what your campaign setting is like, then what you have is a minor tweak to a westmarchian setting. Laying this out up-front is just the usual task of getting on the same page.
However, you do risk changing the style of game, and maybe cheapening the experience if you make things too easy. At the extreme end, an "auto-respawn" effect sets a precedent for playing like a board game or video game where the focus is heavily on battles, looting and exploring, but the sense of risk taking and danger will be largely gone. It might end up a little like a WoW raiding experience - these are still fun, but can miss out on depth that you can get in table-top roleplaying.
At the other extreme, removing life restoration options from the table means removing some player agency that is available in the rulebooks. It should not be necessary to do so. This goes along with "the dice fall where they may" attitude - if the setting supports life restoration and players have made suitable preparations, then they should be rewarded for their efforts.
I would recommend that you have any high status and high level NPCs that the PCs could approach as allies or supporters at least roughly fleshed out at the start of the campaign. Not necessarily full stats, but rough power level, personality, political stance. You don't necessarily want to start a city adventure, but the questions of "Who can help us? Where do we go to get X [any game effect that players look up and want to have for their PCs]?" will crop up quickly in a sandbox setting.
Also, don't rule out some rare friendly wandering NPCs (a Druid grove somewhere on the map perhaps, relatively deep in the map, so that e.g. Level 6 or 7 characters could reach it with some effort) and some very occasional loot (a scroll of Raise Dead). An NPC cleric who cannot Resurrect, but knows that 200 years ago, the priest at the church in the now ruined citadel was so pious that the gods granted them power over life and death, is maybe a suitable pointer for motivated sandbox players to mount an expedition.
A rule of thumb that I have followed in sandbox settings, is that players should be able to access, somehow, one-off spells and powers that are maybe 1-4 character levels (so 1-2 spell levels) higher than they have access to via their own characters, and assuming they tackle suitable challenges in the sandbox. These things should be loot, or require extra work to get. But the rarity and difficulty makes them desirable goals, something to motivate the players.
To my mind, that should mean a team of 7th-level characters may have scored one or two Raise Dead / Reincarnates - as scrolls perhaps, or via a deal with a difficult-to-access NPC. That's just my preferred difficultly level though. A wide range around that exists, and should be fine in any sandbox setting, including westmarchian games. As one of the core tenets is player agency, you need to ensure the information about how revivifying their characters will work is available to them when needed.
