Is built in phono preamp usually best way to go?

Not just for economy but for fidelity as well. Im thinking by having internal phono stage you dont have to buy extra cable, power cord, or housing and power supply etc..... Just for hypothetical analysis lets say you buy a $1500 preamp and a $1500 phono preamp. Would you not under most but not all circumstances be better off with an added $500 phono module in preamp? I know you may not have the extra versatility on settings like a phono preamp would have. I read some where years ago in a magazine its usually best to buy preamp with phono module built in. I know now some preamps dont have phono built in and if they do it might be putin as an after thought like headphone amps. I just bought a Bryston BP25 with MM stage and going to compare it with my Acoustech PH1-P phono preamp. The Bryston is replacing the Adcom GFP-750. From my research it should be an up grade. Also I wanted to see if it has better matching with my Bryston amp. It does not have near as much volume in passive mode and I have to add gain to my phono stage for dynamics but im wondering if im just introducing distortion. High output Benz MC bumped up to 52 gain. I usually favor passive mode because of the Adcoms active stage grain. Im being somewhat critical and its not a bad preamp. Just want an improvement. Any thoughts appreciated
"Just for hypothetical analysis lets say you buy a $1500 preamp and a $1500 phono preamp. Would you not under most but not all circumstances be better off with an added $500 phono module in preamp?"

I know what you are asking, but the simple answer is, your question can't be answered with any type of accuracy. There's just way too many variables. The only advice I can give you is that you need to get the info you need to make the choice yourself. And by info, I mean actual listening. If you do this going only by opinions and reviews, success will probably be accidental.
One issue with a built in phono, is that you don't get as much isolation from all of the other electronics and the power supply of an all-in-one unit. This is particularly important for a phono stage due to the sizes of the signals involved. You'll note that many standalone phono stages employ external power supplies for better performance.
There is no 'best way to go' when it comes to just about anything in audio. Many choose to go built in, whether just with a phono stage in a preamp, or an integrated amp that has a preamp in an amp, because it is more simple and economical.

There are many arguments for going in either direction, but it pretty much boils down to whether you want more flexibility and are happy to pay for it, or whether you want more bang for the buck. It will be a different choice for everyone. What is the right choice for another, will not necessarily be the right choice for you.
No. The issue really is power supplies interfering with the phono stage.
An integrated with phono is going to have a hard time isolating anything but a MM phono section.

If you want a good Moving Coil phono, a separate device is really better.
I own three 'keeper' preamps, and all three have separate power supplies.. The separate power supply really makes the preamp better.
So in the price range the op is discussing.. a separate phono box is a better choice. even with the need for more parts. that those parts are separate IS a sonic plus.
If you found a preamp with a separate power supply and a MC board, that would probably be fine.
There was a time when all preamps, receivers, and integrated amps had built in phono sections and these conversations just didn't occur. You already pulled the trigger and purchased the Acoustech. I would suggest letting your ears decide.
I've owned a few preamps that had great phonostages, the early Levinson(2),a Conrad Johnson Prem 2,Audible Fidelity ,AtmaSphere mp3,all had phono stages that were much better than the most of the pack and I would assume still better most of the add on phono stages in todays gear.

I currently have a Steelhead,and yes it has a massive separate power supply and lots of loading choices,so it's a fun thing to have.

But I have no way of knowing if it's performance is much better than the ones that came before.

Because I don't have the same turntable,or cartridge or anythingelse from those days.

I would suggest that where you decide to invest should be determined by the quality of the turntable, arm and cartridge.

If you have a simple vinyl set up, I don't see the need for separates.Don't forget the cost and variable of the interconnect or extra power cord.

Keep it simple.
Keeping the phono section in the preamp with the line stage is a good move. You avoid the problems of connectors and cable colorations. Connectivity can make or break any system. The phono is likely the highest resolution format currently commonly available; why compromise it??

All you have to do, if worried about power supply noise, is put the power supply in a separate box. If the preamp design is worth its salt (note the caveat), putting the phono section in the box with the line section will offer the least compromise.
Separate will be better, but here is some of my experience to back it up. I owned a Krell preamp with a phono board and then purchased the separate Krell KPE phono which has the exact same board in it, but the KPE was better. It had it's own power supply and was no longer inside of a chassis with a bunch of noise.
As your Bryston already had an inbuilt MM phono stage......have you considered adding a passive SUT for LOMCs instead of considering an 'active' device?
Even though my Halcro DM10 Preamp has both MM and MC active phono stages built in........I just recently tried an SUT into the MM input and was impressed with the improvement.
Of course one has to careful about careful matching and 'in-home' listening would be compulsory IMO?