I don't think white is that weak across the board (i.e. equally weak in all formats).
I have a mono-white Legacy Rebels deck and it is super fun to play. Rarely do I feel behind my opponent and it is super versatile and resilient. Hell, thanks to Tithe, I never even miss a land drop; I always manage to have enough mana to tutor for a specific rebel or rebel card when I need to. Swords to Plowshares is hard to beat for removal. Knight of the Holy Nimbus and Day of Judgment usually makes my opponent's life difficult, acting as a quasi-tax effect and complicating combat math at times.
White in Commander is surely a support colour more than anything, but I wouldn't say it's bad. WotC has been adding elements to white we haven't seen before so they are on a good path to perhaps balancing the colour out for Commander. Heh, maybe Truce and Temporary Truce will see Commander play despite being symmetrical draw spells.
All that being said, other colours clearly have it much easier. I'm looking at you Simic.
I have heard about white being good in other formats that allow for much older cards, making it somewhat viable, however white still has its major downsides.
The main one that comes to mind in card advantage, all other colors have some form of actual card advantage where white can only draw single cards at a time, and just replace the draw spell in hand. Good cards from other colors that come to mind are
Light up the Stage,
Elder Gargaroth, and
Grim Tutor (although some do not see play in formats outside of standard and historic). These to me act as actual card advantage because they are either netting you cards (
Light up the Stage), are stapled to a creature or permanent (
Elder Gargaroth), or find a specific card to solve a problem (
Grim Tutor).
Cards like
Revitalize just replace themself in hand and have a lackluster effect, like in this example gaining 3 life which to most people is not that important. It just feels to me that in the few ways that white is useful, it falls very short in other categories that are just as important to have a strong color.
To address the example of
Tithe I agree this is a strong effect, and is also seen on cards like
Oreskos Explorer, and
Land Tax, but is only truly most effective when you are already behind. Which lets face it you most likely are if you are playing mono white. These effects, excluding
Land Tax, also only fetch
plains cards, making you more likely to have to run mono white, thus limiting yourself again.
If they added more of this effect into white, say in a standard set, or commander set this might become a way for white to thin their deck and more likely hit good cards consistently. This could act as white's "card advantage" but considering this is somewhat what green does already, and does it better I am so-so on the idea overall.
Also just wanted to say that I'm not disagreeing with you in that white can be a strong color, it certainly can. To me it just seems much more limited in its application compared to the other colors of the pie, whereas colors like green can be put into almost any deck effectively.
Final note to round this out. Simic 100% has been getting to many ridiculous cards that do way to much for so little mana *cough* *cough* Uro *cough* *cough*. They also have had lots of
flash in the past couple standard sets as seen in
Wildborn Preserver, and
Nightpack Ambusher.
Flash has not historically been a green type effect, and just adds to the overall power of the color.