Second point: why show it on the first start? People don't trust or like the software at first, so they would just click X and begin using the software. Some would even think it's intrusive.
Rather, I've seen solutions where the software would ask for money right after it's been useful to the user. Duplicati for example would tell you to donate, suggested amounts, right after it successfully restored a backup.
I'm sorry, I believe the article directly contradicts your statement since its mentioned they receive donations outside of GNOME, in platforms such as Liberapay, and it's the only way to pay for actual development.
A perennial issue for GIMP, at least their branding is consistent though :)
User experience is the study in how to optimize an users' experience, so that they can solve issues or tasks faster, easier or better. UX might affect how an app behaves or how it looks but it isn't tightly tied into the visuals of an application. Aesthetics are just a small part of UX but usually a rather big part in UI.
No one donates to software they don't trust. By the time they read the donation banner and consider it, its because they use the software and trust it.
This should be as direct and hassle free as possible, I agree with OP.
So in fact you need to be on Liberapay, Patreon, Tippee, OpenCollective, Paypal, HelloAsso and more in order to be sure you're not going to lose your source of donations from one day to the next. I mean if only every finance services provider was as transparent and benevolent as Liberapay, all would be fine. But we live in a grim world, and even Liberapay was almost shut down due to not finding a suitable finance service provider after Mangopay threw them out.
That's why i truly appreciate when some established non-profits help gather funds for smaller projects. For example, the disroot.org hosting coop redirects some funds to free-software projects they either use directly or encourage their users to use. What i appreciate even more, is when i can donate cash in person to volunteers during free-software conferences, and/or buy a souvenir like a nice t-shirt... That's truly the only way i know where my money is going, cryptocurrencies aside.
Some people have had PayPal accounts for a decade plus, like me. I'm really not about to make a transaction with a random company simply cause I don't need to enter my phone number.