While the main point of having a wedding is to celebrate and share your marriage with your loved ones, everyone knows that an awesome party costs money. Unless you live a Gatsby life, weddings usually mean credit card debt and perhaps even loans. Hence having a budget and spending within your means. Even though most wishing well poems will have something along the lines of "your presence is present enough" we all know that at the end of the day, if you host a wedding celebration you can expect that your guests will bring something with them whether it's a present or money in a card. This is just wedding etiquette passed on from generations.
In my opinion the best way to work out this dilemma is to honestly figure out what you would like to receive on your wedding day. Unless you imply a very strict no presents rule, it's better to have your guests give you something you would want and use rather than a shed full of useless items that you will probably re-gift later on. If you prefer to have cash over anything else then by all means use a wishing well. The fact is that your guests are probably quite close to you and will understand your request. This will also free up their time of looking for a gift for you.
If having a wishing well is not your thing (and that's completely fine) I think a gift registry is a great option where you can choose what items you would like and control how much your guests spend. Most department stores and specialty stores have gift registries so you can choose to your heart's desire. It's sort of a win-win situation for everyone.
Another option is going digital through websites that offer funds like Envelope Registry. It takes the awkwardness out of asking for money and is a great concept!
In conclusion I don't think the wishing well is a terrible thing. It saves your guests a lot of time and wasted money. You can be creative with the text on the wishing well making it a fun thing rather than an awkward request!