Tired of the continuous back problems and the lack of flexibility of my core I'm considering the purchase of an endurance bike, I have the opportunity to take a BMC 01 Roadmachine Five TG 54 which in theory should be endurance; However, looking at the technical details I noticed that it mounts the ICS02 BMC stem that allows the passage of cables internally. The stem is beautiful but there is a problem has a negative inclination of 12 ° is not really an endurance solution.

So I would like to know if you think I should opt for another model


https://www.bmc-switzerland.com/it/stem-ics2-p2p.html

Roadmachine 01 FIVE Endurance Road Bike (bmc-switzerland.com)

Compared to what other bikes you didn't like?

Endurance really isn't a particular set of geometry numbers. It's more what you can comfortably ride. Some can do that in a very aerodynamic position or "race" fit and others need to sit up more.

So knowing what bikes you rode before will help us know if the BMC Roadmachine is any better a geometry to go in the direction you seem to think will make it fit you better.

I didn't look, but I"m guessing the -12° stem angle is to make the stem roughly horizontal to the ground which makes for better aesthetics. if you need a higher bar position you can simply flip it if it's not a integrated stem and bar. Remember the head tube and steerer tube are on a angle too so having no angle on the stem would look weird to many of us.

Me, I'm a geezer with a geezer's viewpoint. I say fix your core, not your bike. Get PT, join a gym, stretch every morning, all of the above, whatever it takes. Human bodies are mostly fixable. My history says that "If it hurts, work it" is a good motto. Besides getting a long happy life, it's cheaper.

OTOH there's a possibility that your current bike is a full race machine with a very large saddle to bar drop, in which case anything will be an improvement for casual riding. IME anything with a saddle to bar drop of less than 10 cm will work fine for very long rides. In my mid-70s, I went from a -17° to a -11° stem, still slammed, though that wasn't really necessary. I've been a gym member since '79.

I'm not a big fan of stem/bar setups which don't allow easy component changes. I know that's getting popular, but IMO it's a mistake. I'm riding a 2000 carbon bike which is still perfect for my long rides in the mountains, partly or maybe mostly because it's been easy to change out components.

I definitely agree with that. Every time my back or any other part of me felt like it had a persistent ache or pain, I was always able to strengthen the muscles around that area with exercises to make that annoyance go away. Particularly back pain.

I realize some people have back pain caused by other real issues such as injury or things like scoliosis, but many don't and just need the exercise directed on that particular part of their body for a time.

I do exercises to strengthen my core daily but due to some pathologies I don't have well developed muscles and I will never have them (I can do thousands of exercises but my core will remain weak).
I have little flexibility in my back and have been told an endurance bike can help.
I had two bikes with endurance geometries, an emonda with h2 geometries and a cannondale synapse and I found a good compromise, then I tried an ostro vam size 54 (55 horizontal tube) but I can't find the position, the same problems persisted presented when I took a specialized tarmac. Beyond the geometries, my feeling has always been that of having a bike that is too big.
For example, all biomechanics say that my ideal size would be a bike with a 54.5cm top tube and an 11cm stem, but I've never always had the feeling of being better on a smaller bike ... size 52 with a 53.5 top too if the height of the head tube is lower precisely because the longer I stretch the more I have back problems

Smaller size in the same model of bike is going to put your bars lower if your saddle is at the proper height on them. Saddle height is the all-important measurement on a road bike that will pretty much be the same for all road bikes you try on no matter the size of the frame.

So I'm having a little trouble understanding why you say you want a more relaxed position but then say that a smaller bike, which shouldn't have given you a more relaxed position, actually felt better. Did you just set the saddle height to be even with the bars or some other such?

Typically it's expected bikes with a higher stack to give you the more relaxed position. But you do also have to consider their effective top tube length or reach from the saddle to bars/hoods. Which will vary somewhat from one model to another and from brand to brand. Though they are similar as most brands build to their average customer dimensions. So if you are an outlier in that, then you might need a custom bike or learn to adjust and change what you need to adjust and change.

Either the bike and stem fit you or they don't. It isn't up to the stem.

Endurance is a vague idea, not a fit, geometry or comfort level.

Specialized still lets you flip the stem on a Roubaix. It comes with a butterfly handlebar, too.