Upgrade advice

I got a hybrid Trek 7000 AL new a number of years back and I am wanting to upgrade the bike to more road bike style handlebars and paddle shifters. I talked to the local bike shop and they advised against it saying the ergonomics wouldn't work out. Would these upgrades be advisable for this bike or should I scrap the idea and start shopping around for a more road oriented one?

 

The nickels and dimes can really add up.

Parts are more expensive when bought separately than on a complete bike.

Even if you wound up saving a little by upgrading your 7000, you'll get a better road bike by buying a complete one.

 

If you can DIY, then you can convert your bike to Drop handlebars & appropriate shifters for UNDER $200 if you opt for Campagnolo shifters ...

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Hybrid frame ...
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MTB frame set up with 700c fork + 700c wheels ...

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Trek 7000s have had both quill stems and threadless stems in their lifespan, each system had two different common sizes where they attach to the frame and several different diameters where they attach to the bar. There's different bar sizes.
Make sure your intended brake levers fit your intended bar,
make sure your intended bar fits your stem,
if you need a new stem make sure you can put it on your fork or find out about the availability and cost of a stem adapter,
add the cost of bar tape and new cables,

 

BTW. The head tube angle on the two examples with the forks which are shown is 73º ... that's pretty "standard" for a Road bike ...

The shop makes a lot more money by selling you a 'new' bike ...
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While those are NOT insignificant caveats, I'm guessing that your bike isn't so old that it has a quill stem ... but, a different length stem may eventually be in the offing (a picture of the specific TREK would probably help) ...

Inexpensive, "generic" OS stems on eBay are certainly ONE PLACE that a person can economize if-and-when the time comes for a different length.​

Of course, garage sale GT is correct that you can end up spending a lot of money IF you were to attempt to make the conversion with either Shimano OR SRAM shifters ... more so for SRAM since you would need both front & rear derailleurs ...

Campagnolo shifters can work with almost any CABLE ACTUATED front derailleur ...

The pictured MTB frame has a TOP PULL, 8-SPEED, XT front derailleur.
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Handlebar tape doesn't have to be expensive.

 

I read all of the comments and all I can say is AHHHHHHHHHH.

NO, don't upgrade your components. There is the bike you want for a lot less than you could upgrade with descent parts and the geometry is totally different between that old Trek and a newer one with Shimano 105 components. Don't think that you can just make that bike better. But also be careful of the idea that anything newer is better. Be conservative.