Strange how those 'opposed' to this concept feel the need to protest again' it so vehemently!
Its your rifle ( and investment ) so ultimately your choice. I would suggest that part of the issue is not grasping what one is trying to achieve - which applies as much to everything else as rifle barrels!
Possibly the only thing that people MAY agree upon is that rifles are quite individualistic - so even between same brands/ models there can be variation. I personally edge with the views per link to Border Barrels - but there are other barrel makers who say different - or so it seems. Some of the makers that speak in opposition, actually refer to their products - which are highly finished before arriving with the customer. Read context as well as content.
Break-in seeks to address the finish on a bore - both in terms of surface make up and ( for want of a better term ) 'edges - eg lands, crown etc. Ultimately the goal is consistency.
In relative terms a rough finish will abrade more jacket material during use and provide a better 'key' for that material and firing residue to bond/ hide in. Firing material in particular can attract moisture, react with it and create compounds that aren't very metal friendly. A super smooth - lets call it the proverbial mirror finish - offers less harbours for crud, but can result in significant increase in friction - purely from increased surface area.
A very poor barrel may have burs and such from the manufacturing process - which strip more material from bullets and can in extremis mark the bullet enough to impact consistency.
The idea behind lapping, break-in et al is to give a helping hand in the right direction. The aim being to create the conditions for best accuracy, longevity, ease of cleaning and so on - often in a mix that interacts with each other.
On a deer rifle it's a fair question to ask how relevant this is. There are very few instances where a sub MOA rifle is the be all and end all if you are potting deer size targets at deer stalking - as opposed to 'Carlos Hathcock re-enactment' ranges. But that same rifle will likely experience damp conditions and many a horror lurks beneath a shiny coating of bullet metal.
Its about choice - informed choice. Dogma contributes very little to debate or decision making - it just feels like it!
That said, I'll be dogmatic and say that more rifles are spoilt through injudicious 'care' than from using.
Done properly, break-in will cause no harm. If you have a super hot calibre with limited barrel life then every round fired significantly contributes to wearing out. For most middle of the road deer calibres the numbers involved are such that the issue isn't anything to sweat over. No hard evidence to hand, but I would hazard that the overall wear saved from a well conditioned bore outweighs rounds fired during break-in type processes.
Some rifles need no work at all, others would benefit from work - be it minor or relatively more extensive. Because we set out by defining what we want to achieve, the issue of how many shots, its pointless because of proof firing, quality rod or bore snake etc will self answer.
Number of shots?
There is no defined number. It depends on the work required to produce the finish you want with the bore you have.
I once helped a guy on the range. He had a brand new rifle and was attempting break-in - as advised by some 'pal'. After a while he was getting wound up because nothing he did would get any copper out of the bore. His groups were running at 1/2-3/4" from a very nice rifle sporting a brand new top of the line Border Barrel. Once he asked for help, we pushed a clean patch in - stopping an inch or so short of the muzzle and peered into the bore. A superb near mirror finish was obvious.
He wasnt seeing any sign of copper because the minute amount that accumulated from a shot wasnt enough to give an obvious reaction on the patches. Aside from his brief puzzlement, there was no waste - he'd sighted in and was producing some 'to be proud of' groups with all the brands of ammo he wanted to use.
To work, the process looks to put a bullet down a pristine barrel - so the jacket, combustion gas, residue etc all acts upon bare metal. Hence cleaning between shots each time. The
proof round was the first shot - before you start shooting, you clean the barrel to metal. It doesnt spoil the process once you appreciate what you are doing.
So some rifles may require zero break-in shots. Unless you know for certain, you lose nothing by at least cleaning before firing and immediately after the first shot.
After that first round, clean using a quality rod in the manner well covered in various places. With a solvent wet patch and the rifle well supported, push the rod through slowly. Make sure there are no distractions and focus on the feedback you get from the rod. Usually you get a slight resistance at the throat, then a slight pause about 9" in, then ok until the last 2" of the bore.
If you get constant stiff resistance ( and assuming you are using the correct size jag and patches ) then thats the fouling gripping the bore. This indicates some more burnishing required.
Get the bore completely clean and fire again.
Repeat. Again read what the bore is saying to you. The throat and 9" point will likely still offer brief resistance. If the bore felt rough along its length, then hopefully its a bit easier this time.
Usually within 5 shots like this you will get a noticeable improvement. In some cases it will be slick the full run of the rod in others there'll be slight resistance - but improving everytime. In the latter case I opt for another few cycles rather than upping to two shots, five shots etc. Its your choice - the important bit is listen to the rod - dont start a conversation with it; that's something completely different and mildly worrying
The bore snake debate has raged elsewhere, so not going to pour petrol ( or bore solvent ) on those flames. But such a system makes feeling what is going on in the bore very difficult.
Is it a faff? Depends on you - some like the process, other loathe it. But its your choice.
From experience, the time invested at the outset is more than recouped in time saved and material costs saved over the lifetime of the rifle.