Negative.
In the modern day you're average grunt is going to be equipped with an assault rifle, whether that means something with 5.56 NATO or an AK-47. Even LMGs now generally pack the same cartridges, probably for logistical reasons as well as fire superiority doctrine. M249, RPK, etc.
But then you've got all this crapola that resulted when NATO and Warsaw militaries realized, wuh-oh, what do we do when we need to engage a target at medium to long range.
Now we've got a whole collapsible chest of calibers like .50 BMG used in HMGs and sniper rifle/anti materiel rifles;
and the 7.62x51's seen a resurgence in NATO with DMRs like the M14 EBR for purposes of intermediate accurate fire;
and finally the 7.62x51's Soviet equivalent, the slightly extended 7.62x54 SVD, which is used as a marksman rifle and is integrated into the Russian military on pretty low levels.
If Wikipoopia is to be believed:
The Dragunov is an original rifle design for several reasons. First, it was not meant for highly trained and specialized sniper teams, but rather for
designated marksmen, spread in every basic infantry unit. In every
platoon of
Warsaw Pact troops, there was a Dragunov rifle marksman.
Take that or research it more, I don't expect you to believe it.
In a nutshell, even modern militaries carry different weapons. For instance 7.62 LMGs are brought it in for heavy fire support in the US military, while 5.56 M249s are used most often in the LMG role. Carbines and full sized AR-15 type rifles are used in the US military to further differentiate. Warsaw has AK-74 and the 74U carbine variant which is very nearly suited for the submachine gun role. For longer range engagements there's a wide assortment of specialized calibers from 7.62 NATO to .50 BMG.
No modern nation sends infantry out equipped entirely with assault rifles, looking stupid until something bad happens. They give a few specialized soldiers cool stuff like LMGs, bigger LMGs, HMGs, DMRs, sniper rifles and anti-materiel rifles.
This variety won't be realistically reduced without the introduction of a low power cartridge with exceptionally good ballistic properties like the 6.5 or some unknown equivalent. The 5.56 sucks for cover penetration, stopping power when it counts, and long range ballistics. The 7.62x39 AK-47 round is clunky and has miserable ballistics.