Is object orientation bad for embedded systems, and why?

What makes you say that C++ is Object Oriented? C++ is multiparadigm, and not all of the features that C++ provides are useful for the embedded market due to their overheads. (So... Just don't use those features! Problem solved!)

Taking your quote at face value, dynamic memory allocation is completely separate concept from object-oriented software design, so it's outright false. You can have object-oriented design, and not use dynamic memory allocation.

In fact, you can do OO in C to an extent (that's what Linux kernel does). The real reason that many embedded developers don't like C++ is that it's very complex and it is hard to write straight-forward and predictable code in it. Linus has a good recent rant on why he does not like C++ (it's better and more reasoned than his old one, I promise). Probably most folks just don't articulate it very well.

Whilst I'm not sure it answers your question, I can summarise the reasons my previous companies source code was pure C.

It's firstly worth summarising the situation:

• we wanted to write a large amount of "core" code that would be highly portable across a large number of ARM embedded systems (mostly mid-range mobile phones; both smart phones and ones running RTOSs of various ages)
• the platforms generally had a workable C compiler, though some for example didn't support floating point "double"s.
• in some cases the platform had a reasonable implementation of the standard library, but in many cases it didn't.
• a C++ compiler was not available on most platforms, and where it was available support for the C++ standard library, STL or exceptions was highly variable.
• debuggers often weren't available (a serial port you could send debug printfs to was considered a luxury)
• we always had access to a reasonable amount of memory, but often not to a reasonable malloc() implementation

Given that, we worked entirely in C, and even then only a restricted set of C 89. The resulting code was highly portable. We often used object orientated concepts though.

These days "embedded" is a very wide definition. It covers everything from 8 bit microprocessors with no RAM or C compilers upto what are essentially high end PCs (albeit not running Microsoft Windows) - I don't know where your project/company sits in that range.