When creating a logo/identity for your business, you don't always have to be to focused in showing what you do though a symbol or imagery too literally.
It's the obvious route which is why you'll have seen lots of piggy banks and wallets but say if you look at many of the world major banks, how many of them have an image or even a suggestion of money?
I can't think of many off the top of my head.
It's about creating something that your potential customers can connect with and you feel gets your image across.
This can be more about use of fonts, colours and abstract imagery.
More of a feeling really.
This is when it is good to employ a good designer that understands this.
I think you're right. Focusing on brands like Twitter and Mailchimp where the symbol is the brand is maybe not the best approach to take. Will take your feedback into consideration when we approach the design.
The logo is probably not something you should even be worrying about. You could have something plain and simple (look at HP's branding with their keystroke rectangle) and it would still do well with customers so long as the actual product/service is right for them and you have people within the business actively selling and marketing it. If your competitors are doing something similar then you obviously need to stand out in other ways, i.e. through the actual quality of the service itself.
Who is the product/service aimed at? Could it be that the generic logos are used because they appeal to a particular market?
You must first assess your business and what you really want to be in that business logo design. You could search for other logo ideas and design to help you, or ask assistance from professional logo designers.
Hey, what i've learned is it is incredibly important to first have a design brief to get a solid idea of what kind of logo/demo graph you're looking for. My buddy showed me this website http://createbrief.com/ it helped me immensely.
Really great advice here, im currently workig with a client who wants a rebrand of there logo and are asking for an 'icon' next to some text to represent what they do as a buisness. im trying to stray away from that and doing it stripped back simplicity at best!