There is also something to be said about how Han might look at the Falcon on a practical level when it comes to how it appears in SOLO as compared to its classic OT and current ST look.
The ship in SOLO, clean, blue detailing, smooth profile etc. just looks too... Good. By that I mean, Han looks at the Falcon as part of his operation as a smuggler, emotional attachments not withstanding. As such he might look at the way the Falcon originally looked and just thought it's not optimal for his purposes looking like a SW equivalent of a high end luxury car with all the cool options.
Let me put it this way... A dumb drug dealer will sell his stuff out of the most eye catching and cool looking car as a balm to his ego. Well... That's just bringing attention to something you'd rather keep on the down low. A smart drug dealer would sell out of a reliable but none to flashy car to stay inconspicuous. So too with our beloved smuggler. Why fly around in a ship that is tricked out to the nines if you are a smuggler wanting to pass unoticed from system to system?