This is not true. But if, as you said, there is no difference between 5000 level and 500, why even bother doing the first one?
The reason for choosing 5000 over 500 is because bigger numbers are more appealing (generally speaking) and easier to balance around. Take for example runescape back in the day, their minimum hit was 0 and maximum hit was like 20. They had a hard time giving players boosts because they could not do anything in between for example 0 and 1. They eventually multiplied damage by 10 so that they could have what would have been an impossible 0.5 be 5. Later they multiplied it by 10 again for even more flexibility. This allowed much smaller power increases to be noticeable by players rather than feeling useless.
Also a few of the things you have stated are simply untrue and/or design decisions that have no correlation with a server being high rate or not.
Higher level means you have higher margin error, more speed & more mana to tank it up (as you probably have higher-valued potions etc).
Not sure what you mean by "higher margin of error".
Higher level does not necessarily mean more speed, in fact speed is only determined by level if you leave it as default. We are talking about custom servers I assume so having a custom speed formula is not unreasonable.
As for the mana/potions, this is the same as my SD example. If a player has 100 mana and heals 10 with a potion on low rate, it is the same as if the player has 1000 mana and heals 100 on high rate, assuming again that damage is also proportional.
It also means that losing a few levels is irrelevant
By default deathloss is a percent of your total experience. This means that the rate at which you gain experience is irrelevant here because you are going to lose the same amount of "time spent leveling" assuming both servers have the same percent deathloss.
so is the cash (in most cases) that you throw here and there as it's not even important at some point.
I know you clarified "in most cases" but I want to say that just because a server has "big numbers" does not necessarily mean that the developers added 99999cc to every monster. Even if they did, the economy can be scaled to fit the amount of gold. An extreme example being OT Chaos back in 7.6 where end-game monsters dropped 30 million gold every kill and yet that server had one of the best economies I have ever seen in an ot.
Also, from a psychological aspect, making progress quick (leveling up fast) is good for a people that want to "do and forget" and making progress slow (leveling up slow) is for people that want to empathize with the character they created (and the other roleplay thingys).
Again, its all proportional. If on real tibia you start at level 1 and the highest level quest is 100 and it takes 6 months to get there, it is the same as a high rate server starting at level 1, the highest quest being level 10000, and it also taking 6 months to get there. It is simply a bigger number, that is all.
There are no clear pros and cons for those two separate paces.
There are actually a few that I can think of off the top of my head.
Pro: Wider range of values to fine tune the balance of a server around.
Pro: Bigger numbers are (in most cases) more appealing to people.
Con: Numbers that are too big start to get cluttered and can get to the point where visually you cannot possibly care about what the actual value is because it's just a series of numbers on your screen (such as incremental/idle/clicker games where you literally deal 458978435972393259375363840 damage)