I have to disagree. It would make the game less skill based and less enjoyable for players. If everyone could see savior count, then the moment anyone used a savior that team would instantly be pressured out by every other team because they know that you had to use a savior and thus are low on army and probably a feed. Everyone is going to be looking to be the one that eats your yummy command centers and merc compounds for bounty. It's not a fun environment to play in when you have to announce to the other 6 players your vulnerability.
However, I do agree with something you said.
I think the more available information that you have in a game means the more strategy involved. Being able to make decisions based off of information is what differentiates bad players from good players.
It's your responsibility as a player, exactly as it is in ladder, to be scouting to get information you can put to use. You have watchtowers, burrowing and cloaked units, scans, observers and general map presence which all help you know what is going on in the map and one of the things you need to know is how many saviors each team has and count them yourself.
Being able to scout and count saviors -is a skill.-
Could you please further explains the hypothetical situation in which it would make the game less skill based?
I mean, say top left pushes bot left early and they are out of saviors, even if the rest of the players try to flush him out then it will end up in them fighting each other and the player with no saviors might even be in a situation to come out on top. It would just add more strategy in getting out the saviors and then using that information to get your opponents out of position so you can come out on top.
Would I rather have a game where a player might be vulnerable and people attacking which would result in a more aggressive and fast paced game or would I like it where 80% of the game is turtling?
It's nearly impossible to keep a constant count on saviors throughout the game, if that's a skill then I don't think anyone possess it as it's not really something a player can constantly and reliably control. Implementing the savior board wouldn't take away from any of the other skills you mentioned, it would magnify them as the game would be more aggressive and fast which would make controlling towers and having good map control more valuable in getting good engagements. It would also give the player with better micro more of an advantage.