I just read What do I need to make a Jewish Wedding. Is there a requirement for seven different people to say each of the seven Brochos, or can one say all of them?
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I heard on a R' Hershel Shachter shiur @yutorah that the older practice was in fact to have one rabbi (often the officiating one) to recite them all. Just as a haftorah or the like has multiple blessings, recited by one person.
In order to spread the honors, today people will often give one (or more) blessings per person. If that works for you, fine; if you want one person to do them all, that's fine too. (But if your cousin's father-in-law's chiropractor's best friend gets upset that he didn't get one, please don't blame me!)
Rabbi Yoel Teitelbaum of Satmar, reacting to the recent divvy-'em-up trend, remarked that pretty soon, they'll have one person say BA and another person say RUCH!
Indeed no Rishonim mention splitting the blessings up among different people. While it's hard to find anyone saying explicitly that one person should say all of them, they probably thought that was obvious and didn't need stating explicitly.
For instance, R Avraham ben HaRambam writes (here) that the custom is to have the 'greatest person present' recite the blessings. He wasn't telling us that one person should do it, for that was obvious, but rather who should be that one person. The Sedei Chemed (Berachot 3:8) says the one who says the blessings should drink from the cup. The Zohar (Tazria 44b) speaks of a Chazan (singular) saying Sheva Brachot for a bride. The Yafeh LaLev (EH 62:6) decries the custom of some to give the greater of the two Chazzanim at a wedding (if two are present) the Ketubbah to read instead of the Sheva Brachot (he even prefers giving the latter to a Kohein!). In fact, one of the earlier responsa defending the recent practice of splitting (She'eilat Shelomo 16) opens with a story about how he was at a meal where they split up the blessings and he was so confused!
In any event, sometime in the last 250 years people started splitting up the blessings. The earliest mentions I know of our in Atzei Arazim 62:1 (pub. 1790) and Shaarei Efraim (footnote to 9:30) (pub. 1832) who both had a custom to split off the last Bracha only (which makes some sense as it's not Semukha LaChavertah, see below) so that one/six can be given to someone from the bride's side and six/one to someone from the groom's side.
This is highly non-intuitive, as (as pointed out by Tosfot Ketubbot 8a sv Shehakol) Sheva Berachot contain Berachot HaSemuchot LeChavroteihem -- blessings which are adjacent to other blessings and 'rely' on the opening ("Barukh Attah...") of the initial blessing in the set. These, (like the blessings in Bentching or those surrounding Keriat Shema) are clearly designed to be said as a unit (see, for example, Mishna Berura OC 194 sk 11), even though it's also well agreed that if you said them out of order you fulfilled your obligation (by Shema: OC 61:3; by Sheva Berachot: Kallah Rabbati 1:1; by Bentching: OC 194:3).
For whatever reason, the custom started spreading, and while no one could say the blessings are invalid (if they can be said out of order, they must not require post facto being said adjacent to the previous one), there hasn't been much enthusiasm for this among the Poskim.
Rav Menashe Klein (Mishneh Halakhot 4:204) defends the practice of splitting up the blessings for those places that have that custom if it is done to honor Talmidei Chakhamim, but says he would never start such a custom Lekhatchila.
Rav Moshe Feinstein (Igrot Moshe EH 1:94) rules that the blessings should not be split up unless there is a specific need.
Rav Ovadia Yosef (Yabia Omeir EH 4:7) that even though generally sets of blessings should Lekhatchila be said as a unit, the need to honor multiple Talmidei Chachamim makes the situation a Bedieved one thereby permitting splitting them. In EH 5:12 he repeats this ruling, cautioning that the various rabbis should all be present up at the Chuppah from the outset to avoid any Hefsek in between the blessings. (Yalkut Yosef brings this ruling but writes strongly against divvying up the blessings to family members who often can't pronounce the words correctly or become too emotional to continue.)
Rav Meir Mazuz (quoted in Birkhat Hashem 4:4:64 footnote 192) strongly discourages splitting the blessings, claiming that true Kavod HaTorah is following the enactments of Chazal (not bringing rabbis to the front of a room).
TLDR: If you have some specific need to split up the blessings to avoid family conflict, to avoid insulting a specific rabbi, or to avoid embarrassing someone, then CYLOR as there is likely room to be lenient. Absent that, the traditional practice has always been to have one person say all of them.
The minhag by Chassidim is if the Rebbe or a Rov is there, he says all the Brochos.
At my wedding, the rav / mesader kiddushin did all the brachot. Practical reasons:
That last item may sound incredulous, but, this was really the case. I'm not stating that this is a concern for most people, but, it very well might be.
Also, while most people are glad to attend your wedding (some, interestingly, are not, but come, anyway - I can't figure that out), almost no one likes a chuppah that's longer than necessary. People become impatient after a while. I can't say why, nor do I find such attitude correct (really? 5 minutes longer makes people impatient??), but that's what it often is.